Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/analysis/   (Beweissystem der NASA Version 6.0.9©)  Datei vom 28.9.2014 mit Größe 759 kB image not shown  

Quelle  unif_cont_fun.prf

  Sprache: Lisp
 

(unif_cont_fun
 (getem_scaf4 0
  (getem_scaf4-1 nil 3324907658
   ("" (skosimp*)
    ((""
      (inst 1
       "(LAMBDA (j: posnat): choose({xy: [real,real] | P3!1(xy`1,xy`2,j)})`1)"
       "(LAMBDA (j: posnat): choose({xy: [real,real] |  P3!1(xy`1,xy`2,j)})`2)")
      (("1" (skosimp*)
        (("1" (inst -1 "k!1") (("1" (assertnil nil)) nil)) nil)
       ("2" (skosimp*)
        (("2" (expand "nonempty?")
          (("2" (expand "empty?")
            (("2" (expand "member")
              (("2" (inst -2 "j!1")
                (("2" (skosimp*) (("2" (inst -1 "(x!1,y!1)"nil nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((P3!1 skolem-const-decl "[[real, real, posnat] -> bool]"
     unif_cont_fun nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (choose const-decl "(p)" sets nil)
    (member const-decl "bool" sets nil)
    (empty? const-decl "bool" sets nil))
   nil))
 (unif_cont_interval 0
  (unif_cont_interval-5 "FIX" 3447507474
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (expand "uniformly_continuous?")
          (("" (skosimp*)
            ((""
              (case "EXISTS (N: posnat): FORALL (x, y: ({xx: T | a!1 <= xx AND xx <= b!1})):
                        abs(x - y) < 1/N IMPLIES abs(f!1(x) - f!1(y)) < epsi!1")
              (("1" (skosimp*) (("1" (inst + "1/N!1"nil nil)) nil)
               ("2" (hide 2)
                (("2"
                  (case "EXISTS (eps: posreal): FORALL (N: posnat):
                          EXISTS (x, y: ({xx: T | a!1 <= xx AND xx <= b!1})):
                            abs(x - y) < 1 / N AND abs(f!1(x) - f!1(y)) >= eps")
                  (("1" (skosimp*)
                    (("1" (hide 1)
                      (("1" (lemma "getem_scaf4")
                        (("1"
                          (inst -1
                           "(LAMBDA (x,y: real,n:posnat): abs(x - y) < 1 / n AND a!1 <= x AND x <= b!1 AND a!1 <= y AND y <= b!1 AND abs(f!1(x) - f!1(y)) >= eps!1)")
                          (("1" (split -1)
                            (("1" (hide -2)
                              (("1"
                                (skosimp*)
                                (("1"
                                  (name
                                   "A"
                                   "(LAMBDA (kk: posnat): {xx: real | EXISTS (j: posnat): j >= kk AND xx = XX!1(j)})")
                                  (("1"
                                    (name
                                     "alpha"
                                     "(LAMBDA (kk: posnat): lub(A(kk)))")
                                    (("1"
                                      (name
                                       "CC"
                                       "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                      (("1"
                                        (case
                                         "a!1 <= CC AND CC <= b!1")
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (rewrite
                                             "continuous_on_def")
                                            (("1"
                                              (inst -8 "CC")
                                              (("1"
                                                (expand "convergence")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst -9 "eps!1/2")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (expand
                                                         "extend")
                                                        (("1"
                                                          (case
                                                           "EXISTS (kk: posnat): CC <= alpha(kk) AND alpha(kk) < CC + delta!1/2 AND 1/kk < delta!1/2")
                                                          (("1"
                                                            (skosimp*)
                                                            (("1"
                                                              (case
                                                               "EXISTS (nn: posnat): alpha(kk!1) - delta!1/2 < XX!1(nn) AND XX!1(nn) <= alpha(kk!1) AND nn >= kk!1")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   -12
                                                                   "nn!1")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "1/nn!1 < delta!1/2")
                                                                      (("1"
                                                                        (case
                                                                         "CC - delta!1/2 <= XX!1(nn!1) AND XX!1(nn!1) <= CC + delta!1/2")
                                                                        (("1"
                                                                          (case
                                                                           "CC - delta!1 < YY!1(nn!1) AND YY!1(nn!1) < CC + delta!1")
                                                                          (("1"
                                                                            (flatten)
                                                                            (("1"
                                                                              (lemma
                                                                               "triangle")
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "f!1(XX!1(nn!1)) -f!1(CC)"
                                                                                 "f!1(CC) - f!1(YY!1(nn!1))")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (inst-cp
                                                                                     -26
                                                                                     "XX!1(nn!1)")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -26
                                                                                       "YY!1(nn!1)")
                                                                                      (("1"
                                                                                        (split
                                                                                         -26)
                                                                                        (("1"
                                                                                          (split
                                                                                           -27)
                                                                                          (("1"
                                                                                            (hide
                                                                                             -4
                                                                                             -5
                                                                                             -7
                                                                                             -8
                                                                                             -9
                                                                                             -11)
                                                                                            (("1"
                                                                                              (case-replace
                                                                                               "abs(f!1(CC) - f!1(YY!1(nn!1))) = abs(f!1(YY!1(nn!1))-f!1(CC))")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                nil
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide-all-but
                                                                                                 1)
                                                                                                (("2"
                                                                                                  (grind)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("3"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("4"
                                                                                            (hide-all-but
                                                                                             (-5
                                                                                              -6
                                                                                              1))
                                                                                            (("4"
                                                                                              (name-replace
                                                                                               "xxnn"
                                                                                               "XX!1(nn!1)")
                                                                                              (("4"
                                                                                                (grind)
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("3"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("4"
                                                                                          (hide-all-but
                                                                                           (-2
                                                                                            -3
                                                                                            1))
                                                                                          (("4"
                                                                                            (name-replace
                                                                                             "yynn"
                                                                                             "YY!1(nn!1)")
                                                                                            (("4"
                                                                                              (grind)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (lemma
                                                                                   "connected_domain")
                                                                                  (("2"
                                                                                    (expand
                                                                                     "connected?")
                                                                                    (("2"
                                                                                      (inst
                                                                                       -
                                                                                       "a!1"
                                                                                       "b!1"
                                                                                       "CC")
                                                                                      (("2"
                                                                                        (assert)
                                                                                        nil
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -14
                                                                              1))
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (grind)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -3
                                                                              -5
                                                                              -6
                                                                              -7
                                                                              -8
                                                                              -9
                                                                              1))
                                                                            (("2"
                                                                              (name-replace
                                                                               "xxnn"
                                                                               "XX!1(nn!1)")
                                                                              (("2"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-3
                                                                              -6
                                                                              1))
                                                                            (("2"
                                                                              (case
                                                                               "1/nn!1 <= 1/kk!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("2"
                                                                                (hide
                                                                                 -2
                                                                                 2)
                                                                                (("2"
                                                                                  (cross-mult
                                                                                   1)
                                                                                  nil
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide
                                                                 -9
                                                                 -11
                                                                 -12)
                                                                (("2"
                                                                  (typepred
                                                                   "lub(A(kk!1))")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (inst
                                                                         -2
                                                                         "alpha(kk!1)- delta!1 / 2")
                                                                        (("1"
                                                                          (split
                                                                           -2)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -10
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          (("2"
                                                                                            (replace
                                                                                             -2)
                                                                                            (("2"
                                                                                              (hide
                                                                                               -2)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "CC <= XX!1(j!1)")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -10
                                                                                                     *
                                                                                                     rl)
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -
                                                                                                         "XX!1(j!1)")
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (inst
                                                                                                   -
                                                                                                   "XX!1(j!1)")
                                                                                                  (("2"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (hide
                                                                     2)
                                                                    (("2"
                                                                      (prop)
                                                                      (("1"
                                                                        (expand
                                                                         "nonempty?")
                                                                        (("1"
                                                                          (expand
                                                                           "empty?")
                                                                          (("1"
                                                                            (expand
                                                                             "member")
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (inst
                                                                                   -1
                                                                                   "XX!1(kk!1)")
                                                                                  (("1"
                                                                                    (inst
                                                                                     +
                                                                                     "kk!1")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (expand
                                                                         "bounded_above?")
                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -9
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (reveal
                                                                                         -1)
                                                                                        (("2"
                                                                                          (inst
                                                                                           -1
                                                                                           "j!1")
                                                                                          (("2"
                                                                                            (assert)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (typepred
                                                             "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                                            (("2"
                                                              (expand
                                                               "greatest_lower_bound?")
                                                              (("2"
                                                                (flatten)
                                                                (("2"
                                                                  (expand
                                                                   "lower_bound?")
                                                                  (("2"
                                                                    (replace
                                                                     -5
                                                                     -)
                                                                    (("2"
                                                                      (inst
                                                                       -2
                                                                       "CC+delta!1/2")
                                                                      (("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (skosimp*)
                                                                          (("2"
                                                                            (typepred
                                                                             "s!1")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (case
                                                                                 "FORALL (ii: posnat): ii >= jj!1 IMPLIES alpha(ii) <= alpha(jj!1)")
                                                                                (("1"
                                                                                  (case
                                                                                   "(EXISTS (jk: posnat): jk >= jj!1 AND 1/jk < delta!1/2)")
                                                                                  (("1"
                                                                                    (skosimp*)
                                                                                    (("1"
                                                                                      (inst
                                                                                       2
                                                                                       "jk!1")
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (inst
                                                                                           -3
                                                                                           "jk!1")
                                                                                          (("1"
                                                                                            (assert)
                                                                                            (("1"
                                                                                              (inst
                                                                                               -5
                                                                                               "alpha(jk!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "jk!1")
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (hide-all-but
                                                                                     1)
                                                                                    (("2"
                                                                                      (lemma
                                                                                       "archimedean")
                                                                                      (("2"
                                                                                        (inst
                                                                                         -1
                                                                                         "delta!1/2")
                                                                                        (("2"
                                                                                          (skosimp*)
                                                                                          (("2"
                                                                                            (inst
                                                                                             +
                                                                                             "max(jj!1,n!1)")
                                                                                            (("2"
                                                                                              (expand
                                                                                               "max")
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (ground)
                                                                                                  (("2"
                                                                                                    (case
                                                                                                     "1/jj!1 <= 1/n!1")
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      nil
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (cross-mult
                                                                                                       1)
                                                                                                      nil
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (hide
                                                                                   -1
                                                                                   -2
                                                                                   -3
                                                                                   -4
                                                                                   -5
                                                                                   -10
                                                                                   -11
                                                                                   2
                                                                                   3)
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                                                                                       -2
                                                                                       *
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                                                                                          (replace
                                                                                           -3
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                                                                                           rl)
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                                                                                             -2
                                                                                             -3)
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                                                                                                (case
                                                                                                 "(FORALL (A,B: (bounded_above?)): subset?(A,B) IMPLIES
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                                                                                                                     -4
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                                                                                                    nil)
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                                                                                                     2)
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                                                                                                               -1
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                                                                                                                     -4
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                                                                                                   2)
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                                                                                                                 -4
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                                                                                                                                 -5
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                                                                                                                                   -2
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                                                                                                        nil))
                                                                                                      nil))
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                                                         -1
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                                                         "CC")
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                                                       -1
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                                                               -3
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                                                                         -5
                                                                         *
                                                                         rl)
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                                                                            (hide
                                                                             -5)
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                                                                               -5
                                                                               *
                                                                               rl)
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                                                                                 -5)
                                                                                (("1"
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                                                                                     -2
                                                                                     -3
                                                                                     -4)
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                                                                                               -1
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                                                                                                   -4
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                                                                                                 -1
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                                                                                                       -4
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                                                             -4
                                                             *
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                                                                       -2
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                                                                                (hide
                                                                                 -4
                                                                                 -5
                                                                                 -6)
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                                                                                   -4
                                                                                   -
                                                                                   rl)
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                                                                                         -5
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                                                       ("2"
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                                                       -2
                                                       -1
                                                       rl)
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                                                            (replace
                                                             -2
                                                             -1
                                                             rl)
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                                                                     "least_upper_bound?")
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                                                                         -3
                                                                         *
                                                                         rl)
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                                                                           -3)
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                                                                                 -1
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                                                                                   -3
                                                                                   "jj!1")
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                                                                                   +
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                                                                             -1
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                                                                                   -4
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                                        (prop)
                                        (("1"
                                          (expand "nonempty?")
                                          (("1"
                                            (expand "empty?")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (replace -2 -1 rl)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst
                                                     -1
                                                     "XX!1(kk!1)")
                                                    (("1"
                                                      (assert)
                                                      (("1"
                                                        (inst + "kk!1")
                                                        (("1"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (expand "bounded_above?")
                                          (("2"
                                            (expand "upper_bound?")
                                            (("2"
                                              (inst + "b!1")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (typepred "s!1")
                                                  (("2"
                                                    (replace -2 -1 rl)
                                                    (("2"
                                                      (hide -2)
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (skosimp*)
                                                          (("2"
                                                            (inst
                                                             -3
                                                             "j!1")
                                                            (("2"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (skosimp*)
                              (("2"
                                (inst -1 "n!1")
                                (("2"
                                  (skosimp*)
                                  (("2"
                                    (inst + "x!1" "y!1")
                                    (("2" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (skosimp*)
                            (("2" (lemma "connected_domain")
                              (("2"
                                (assert)
                                (("2"
                                  (expand "connected?")
                                  (("2"
                                    (inst -1 "a!1" "b!1" "y!1")
                                    (("2" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("3" (skosimp*)
                            (("3" (lemma "connected_domain")
                              (("3"
                                (assert)
                                (("3"
                                  (expand "connected?")
                                  (("3"
                                    (inst -1 "a!1" "b!1" "x!1")
                                    (("3" (assertnil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (inst + "epsi!1")
                    (("2" (skosimp*)
                      (("2" (inst 2 "N!1")
                        (("2" (skosimp*)
                          (("2" (inst + "x!1" "y!1")
                            (("2" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (uniformly_continuous? const-decl "bool" unif_cont_fun nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (abs const-decl "{n: nonneg_real | n >= m AND n >= -m}" real_defs
         nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (< const-decl "bool" reals nil)
    (IMPLIES const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (T formal-subtype-decl nil unif_cont_fun nil)
    (T_pred const-decl "[real -> boolean]" unif_cont_fun nil)
    (posnat nonempty-type-eq-decl nil integers nil)
    (> const-decl "bool" reals nil)
    (nonneg_int nonempty-type-eq-decl nil integers nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (int nonempty-type-eq-decl nil integers nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (b!1 skolem-const-decl "T" unif_cont_fun nil)
    (a!1 skolem-const-decl "T" unif_cont_fun nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (bounded_below? const-decl "bool" bounded_real_defs nil)
    (greatest_lower_bound? const-decl "bool" bounded_real_defs nil)
    (glb const-decl "{x | greatest_lower_bound?(x, SB)}"
     bounded_real_defs nil)
    (jj!1 skolem-const-decl "posnat" unif_cont_fun nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (A skolem-const-decl "[posnat -> [real -> boolean]]" unif_cont_fun
     nil)
    (alpha skolem-const-decl
     "[kk: posnat -> {x | least_upper_bound?(x, A(kk))}]" unif_cont_fun
     nil)
    (CC skolem-const-decl "{x |
         greatest_lower_bound?(x,
                               {alphs: real |
                                  EXISTS (jj: posnat): alphs = alpha(jj)})}"
     unif_cont_fun nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (triangle formula-decl nil real_props nil)
    (connected_domain formula-decl nil unif_cont_fun nil)
    (connected? const-decl "bool" deriv_domain_def nil)
    (nnreal_plus_nnreal_is_nnreal application-judgement "nnreal"
     real_types nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (div_mult_pos_le1 formula-decl nil real_props nil)
    (div_mult_pos_le2 formula-decl nil real_props nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (posint_times_posint_is_posint application-judgement "posint"
     integers nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (times_div2 formula-decl nil real_props nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (upper_bound? const-decl "bool" bounded_real_defs nil)
    (empty? const-decl "bool" sets nil)
    (member const-decl "bool" sets nil)
    (lower_bound? const-decl "bool" bounded_real_defs nil)
    (B!1 skolem-const-decl "(bounded_above?)" unif_cont_fun nil)
    (A!1 skolem-const-decl "(bounded_above?)" unif_cont_fun nil)
    (s!2 skolem-const-decl "(A!1)" unif_cont_fun nil)
    (ii!1 skolem-const-decl "posnat" unif_cont_fun nil)
    (XX!1 skolem-const-decl "[posnat -> real]" unif_cont_fun nil)
    (jj!1 skolem-const-decl "posnat" unif_cont_fun nil)
    (subset_is_partial_order name-judgement "(partial_order?[set[T]])"
     sets_lemmas nil)
    (subset? const-decl "bool" sets nil)
    (jk!1 skolem-const-decl "posnat" unif_cont_fun nil)
    (archimedean formula-decl nil real_props nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (posint_max application-judgement "{k: posint | i <= k AND j <= k}"
     real_defs nil)
    (posrat_max application-judgement "{s: posrat | s >= q AND s >= r}"
     real_defs nil)
    (extend const-decl "R" extend nil)
    (posreal_div_posreal_is_posreal application-judgement "posreal"
     real_types nil)
    (convergence const-decl "bool" convergence_functions nil)
    (continuous_on_def formula-decl nil continuous_functions nil)
    (setof type-eq-decl nil defined_types nil)
    (jj!1 skolem-const-decl "posnat" unif_cont_fun nil)
    (lub const-decl "{x | least_upper_bound?(x, SA)}" bounded_real_defs
     nil)
    (bounded_above? const-decl "bool" bounded_real_defs nil)
    (least_upper_bound? const-decl "bool" bounded_real_defs nil)
    (nonempty? const-decl "bool" sets nil)
    (set type-eq-decl nil sets nil)
    (getem_scaf4 formula-decl nil unif_cont_fun nil))
   nil)
  (OWRE "FIX" 3399972727
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (expand "uniformly_continuous?")
          (("" (skosimp*)
            ((""
              (case "EXISTS (N: posnat): FORALL (x, y: ({xx: T | a!1 <= xx AND xx <= b!1})):
          abs(x - y) < 1/N IMPLIES abs(f!1(x) - f!1(y)) < epsi!1")
              (("1" (skosimp*) (("1" (inst + "1/N!1"nil nil)) nil)
               ("2" (hide 2)
                (("2"
                  (case "EXISTS (eps: posreal): FORALL (N: posnat):
        EXISTS (x, y: ({xx: T | a!1 <= xx AND xx <= b!1})):
          abs(x - y) < 1 / N IMPLIES abs(f!1(x) - f!1(y)) >= eps")
                  (("1" (skosimp*)
                    (("1" (hide 1)
                      (("1" (lemma "getem_scaf4")
                        (("1"
                          (inst -1
                           "(LAMBDA (x,y: real,n:posnat): abs(x - y) < 1 / n AND a!1 <= x AND x <= b!1 AND a!1 <= y AND y <= b!1 AND abs(f!1(x) - f!1(y)) >= eps!1)")
                          (("1" (split -1)
                            (("1" (hide -2)
                              (("1"
                                (skosimp*)
                                (("1"
                                  (name
                                   "A"
                                   "(LAMBDA (kk: posnat): {xx: real | EXISTS (j: posnat): j >= kk AND xx = XX!1(j)})")
                                  (("1"
                                    (name
                                     "alpha"
                                     "(LAMBDA (kk: posnat): lub(A(kk)))")
                                    (("1"
                                      (name
                                       "CC"
                                       "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                      (("1"
                                        (case
                                         "a!1 <= CC AND CC <= b!1")
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (expand "continuous?")
                                            (("1"
                                              (inst -8 "CC")
                                              (("1"
                                                (expand "convergence")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst -9 "eps!1/2")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (expand
                                                         "extend")
                                                        (("1"
                                                          (case
                                                           "EXISTS (kk: posnat): CC <= alpha(kk) AND alpha(kk) < CC + delta!1/2 AND 1/kk < delta!1/2")
                                                          (("1"
                                                            (skosimp*)
                                                            (("1"
                                                              (case
                                                               "EXISTS (nn: posnat): alpha(kk!1) - delta!1/2 < XX!1(nn) AND XX!1(nn) <= alpha(kk!1) AND nn >= kk!1")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   -12
                                                                   "nn!1")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "1/nn!1 < delta!1/2")
                                                                      (("1"
                                                                        (case
                                                                         "CC - delta!1/2 <= XX!1(nn!1) AND XX!1(nn!1) <= CC + delta!1/2")
                                                                        (("1"
                                                                          (case
                                                                           "CC - delta!1 < YY!1(nn!1) AND YY!1(nn!1) < CC + delta!1")
                                                                          (("1"
                                                                            (flatten)
                                                                            (("1"
                                                                              (lemma
                                                                               "triangle")
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "f!1(XX!1(nn!1)) -f!1(CC)"
                                                                                 "f!1(CC) - f!1(YY!1(nn!1))")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (inst-cp
                                                                                     -26
                                                                                     "XX!1(nn!1)")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -26
                                                                                       "YY!1(nn!1)")
                                                                                      (("1"
                                                                                        (split
                                                                                         -26)
                                                                                        (("1"
                                                                                          (split
                                                                                           -27)
                                                                                          (("1"
                                                                                            (hide
                                                                                             -4
                                                                                             -5
                                                                                             -7
                                                                                             -8
                                                                                             -9
                                                                                             -11)
                                                                                            (("1"
                                                                                              (case-replace
                                                                                               "abs(f!1(CC) - f!1(YY!1(nn!1))) = abs(f!1(YY!1(nn!1))-f!1(CC))")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                nil
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide-all-but
                                                                                                 1)
                                                                                                (("2"
                                                                                                  (grind)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("3"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("4"
                                                                                            (hide-all-but
                                                                                             (-5
                                                                                              -6
                                                                                              1))
                                                                                            (("4"
                                                                                              (name-replace
                                                                                               "xxnn"
                                                                                               "XX!1(nn!1)")
                                                                                              (("4"
                                                                                                (grind)
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("3"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("4"
                                                                                          (hide-all-but
                                                                                           (-2
                                                                                            -3
                                                                                            1))
                                                                                          (("4"
                                                                                            (name-replace
                                                                                             "yynn"
                                                                                             "YY!1(nn!1)")
                                                                                            (("4"
                                                                                              (grind)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (lemma
                                                                                   "connected_domain")
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "a!1"
                                                                                     "b!1"
                                                                                     "CC")
                                                                                    (("2"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -14
                                                                              1))
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (grind)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -3
                                                                              -5
                                                                              -6
                                                                              -7
                                                                              -8
                                                                              -9
                                                                              1))
                                                                            (("2"
                                                                              (name-replace
                                                                               "xxnn"
                                                                               "XX!1(nn!1)")
                                                                              (("2"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-3
                                                                              -6
                                                                              1))
                                                                            (("2"
                                                                              (case
                                                                               "1/nn!1 <= 1/kk!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("2"
                                                                                (hide
                                                                                 -2
                                                                                 2)
                                                                                (("2"
                                                                                  (cross-mult
                                                                                   1)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide
                                                                 -9
                                                                 -11
                                                                 -12)
                                                                (("2"
                                                                  (typepred
                                                                   "lub(A(kk!1))")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (inst
                                                                         -2
                                                                         "alpha(kk!1)- delta!1 / 2")
                                                                        (("1"
                                                                          (split
                                                                           -2)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (expand
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                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -10
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
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                                                                                        (("2"
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                                                                                          (("2"
                                                                                            (replace
                                                                                             -2)
                                                                                            (("2"
                                                                                              (hide
                                                                                               -2)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "CC <= XX!1(j!1)")
                                                                                                (("1"
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                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -10
                                                                                                     *
                                                                                                     rl)
                                                                                                    (("1"
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                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -
                                                                                                         "XX!1(j!1)")
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                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (inst
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                                                                                                   "XX!1(j!1)")
                                                                                                  (("2"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (hide
                                                                     2)
                                                                    (("2"
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                                                                      (("1"
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                                                                         "nonempty?")
                                                                        (("1"
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                                                                          (("1"
                                                                            (expand
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                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
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                                                                                   -1
                                                                                   "XX!1(kk!1)")
                                                                                  (("1"
                                                                                    (inst
                                                                                     +
                                                                                     "kk!1")
                                                                                    (("1"
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                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
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                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
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                                                                            (("2"
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                                                                              (("2"
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                                                                                (("2"
                                                                                  (replace
                                                                                   -9
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
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                                                                                    (("2"
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                                                                                      (("2"
                                                                                        (reveal
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                                                                                        (("2"
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                                                                                           -1
                                                                                           "j!1")
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                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
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                                                            (("2"
                                                              (expand
                                                               "greatest_lower_bound?")
                                                              (("2"
                                                                (flatten)
                                                                (("2"
                                                                  (expand
                                                                   "lower_bound?")
                                                                  (("2"
                                                                    (replace
                                                                     -5
                                                                     -)
                                                                    (("2"
                                                                      (inst
                                                                       -2
                                                                       "CC+delta!1/2")
                                                                      (("2"
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                                                                          (("2"
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                                                                            (("2"
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                                                                                (("1"
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                                                                                   "(EXISTS (jk: posnat): jk >= jj!1 AND 1/jk < delta!1/2)")
                                                                                  (("1"
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                                                                                    (("1"
                                                                                      (inst
                                                                                       2
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                                                                                      (("1"
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                                                                                        (("1"
                                                                                          (inst
                                                                                           -3
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                                                                                          (("1"
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                                                                                            (("1"
                                                                                              (inst
                                                                                               -5
                                                                                               "alpha(jk!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "jk!1")
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (hide-all-but
                                                                                     1)
                                                                                    (("2"
                                                                                      (lemma
                                                                                       "archimedean")
                                                                                      (("2"
                                                                                        (inst
                                                                                         -1
                                                                                         "delta!1/2")
                                                                                        (("2"
                                                                                          (skosimp*)
                                                                                          (("2"
                                                                                            (inst
                                                                                             +
                                                                                             "max(jj!1,n!1)")
                                                                                            (("2"
                                                                                              (expand
                                                                                               "max")
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (ground)
                                                                                                  (("2"
                                                                                                    (case
                                                                                                     "1/jj!1 <= 1/n!1")
                                                                                                    (("1"
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                                                                                                      nil
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (cross-mult
                                                                                                       1)
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (hide
                                                                                   -1
                                                                                   -2
                                                                                   -3
                                                                                   -4
                                                                                   -5
                                                                                   -10
                                                                                   -11
                                                                                   2
                                                                                   3)
                                                                                  (("2"
                                                                                    (skosimp*)
                                                                                    (("2"
                                                                                      (replace
                                                                                       -2
                                                                                       *
                                                                                       rl)
                                                                                      (("2"
                                                                                        (assert)
                                                                                        (("2"
                                                                                          (replace
                                                                                           -3
                                                                                           *
                                                                                           rl)
                                                                                          (("2"
                                                                                            (hide
                                                                                             -2
                                                                                             -3)
                                                                                            (("2"
                                                                                              (assert)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "(FORALL (A,B: (bounded_above?)): subset?(A,B) IMPLIES
                                                                                                                                                                                                                  lub(A) <= lub(B))")
                                                                                                (("1"
                                                                                                  (inst?)
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    (("1"
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                                                                                                         "subset?")
                                                                                                        (("1"
                                                                                                          (expand
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                                                                                                          (("1"
                                                                                                            (skosimp*)
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               +
                                                                                                               "j!1")
                                                                                                              (("1"
                                                                                                                (assert)
                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil)
                                                                                                   ("2"
                                                                                                    (hide
                                                                                                     2)
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                                                                                                        (expand
                                                                                                         "nonempty?")
                                                                                                        (("1"
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                                                                                                          (("1"
                                                                                                            (expand
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                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "XX!1(jj!1)")
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "jj!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (expand
                                                                                                         "bounded_above?")
                                                                                                        (("2"
                                                                                                          (inst
                                                                                                           +
                                                                                                           "b!1")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "upper_bound?")
                                                                                                            (("2"
                                                                                                              (skosimp*)
                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "s!2")
                                                                                                                (("2"
                                                                                                                  (skosimp*)
                                                                                                                  (("2"
                                                                                                                    (inst
                                                                                                                     -4
                                                                                                                     "j!1")
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil)
                                                                                                   ("3"
                                                                                                    (hide
                                                                                                     2)
                                                                                                    (("3"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "nonempty?")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "empty?")
                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "member")
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "XX!1(ii!1)")
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "ii!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
                                                                                                        (expand
                                                                                                         "bounded_above?")
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "upper_bound?")
                                                                                                          (("2"
                                                                                                            (inst
                                                                                                             +
                                                                                                             "b!1")
                                                                                                            (("2"
                                                                                                              (skosimp*)
                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "s!2")
                                                                                                                (("2"
                                                                                                                  (skosimp*)
                                                                                                                  (("2"
                                                                                                                    (inst
                                                                                                                     -4
                                                                                                                     "j!1")
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (hide
                                                                                                   2)
                                                                                                  (("2"
                                                                                                    (skosimp*)
                                                                                                    (("2"
                                                                                                      (hide
                                                                                                       -2
                                                                                                       -3
                                                                                                       -4)
                                                                                                      (("2"
                                                                                                        (typepred
                                                                                                         "lub(A!1)")
                                                                                                        (("2"
                                                                                                          (typepred
                                                                                                           "lub(B!1)")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "least_upper_bound?")
                                                                                                            (("2"
                                                                                                              (flatten)
                                                                                                              (("2"
                                                                                                                (inst
                                                                                                                 -4
                                                                                                                 "lub(B!1)")
                                                                                                                (("2"
                                                                                                                  (assert)
                                                                                                                  (("2"
                                                                                                                    (hide
                                                                                                                     2)
                                                                                                                    (("2"
                                                                                                                      (expand
                                                                                                                       "upper_bound?")
                                                                                                                      (("2"
                                                                                                                        (skosimp*)
                                                                                                                        (("2"
                                                                                                                          (typepred
                                                                                                                           "s!2")
                                                                                                                          (("2"
                                                                                                                            (expand
                                                                                                                             "subset?")
                                                                                                                            (("2"
                                                                                                                              (expand
                                                                                                                               "member")
                                                                                                                              (("2"
                                                                                                                                (inst
                                                                                                                                 -5
                                                                                                                                 "s!2")
                                                                                                                                (("2"
                                                                                                                                  (inst
                                                                                                                                   -2
                                                                                                                                   "s!2")
                                                                                                                                  (("2"
                                                                                                                                    (assert)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (expand "extend")
                                                (("2"
                                                  (ground)
                                                  (("2"
                                                    (lemma
                                                     "connected_domain")
                                                    (("2"
                                                      (inst
                                                       -1
                                                       "a!1"
                                                       "b!1"
                                                       "CC")
                                                      (("2"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (assert)
                                          (("2"
                                            (hide -6)
                                            (("2"
                                              (typepred
                                               "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                              (("2"
                                                (expand
                                                 "greatest_lower_bound?")
                                                (("2"
                                                  (flatten)
                                                  (("2"
                                                    (expand
                                                     "lower_bound?")
                                                    (("2"
                                                      (inst
                                                       -1
                                                       "alpha(1)")
                                                      (("1"
                                                        (replace -3)
                                                        (("1"
                                                          (case
                                                           "alpha(1) <= b!1")
                                                          (("1"
                                                            (assert)
                                                            (("1"
                                                              (inst
                                                               -3
                                                               "a!1")
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (skosimp*)
                                                                  (("1"
                                                                    (typepred
                                                                     "s!1")
                                                                    (("1"
                                                                      (skosimp*)
                                                                      (("1"
                                                                        (replace
                                                                         -5
                                                                         *
                                                                         rl)
                                                                        (("1"
                                                                          (assert)
                                                                          (("1"
                                                                            (hide
                                                                             -5)
                                                                            (("1"
                                                                              (replace
                                                                               -5
                                                                               *
                                                                               rl)
                                                                              (("1"
                                                                                (hide
                                                                                 -5)
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (hide
                                                                                     -2
                                                                                     -3
                                                                                     -4)
                                                                                    (("1"
                                                                                      (typepred
                                                                                       "lub({xx: real | EXISTS (j: posnat): j >= jj!1 AND xx = XX!1(j)})")
                                                                                      (("1"
                                                                                        (expand
                                                                                         "least_upper_bound?")
                                                                                        (("1"
                                                                                          (flatten)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "upper_bound?")
                                                                                            (("1"
                                                                                              (inst
                                                                                               -1
                                                                                               "XX!1(jj!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -4
                                                                                                   "jj!1")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (inst
                                                                                                 +
                                                                                                 "jj!1")
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (prop)
                                                                                        (("1"
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                                                                                           "nonempty?")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "empty?")
                                                                                            (("1"
                                                                                              (expand
                                                                                               "member")
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -1
                                                                                                 "XX!1(jj!1)")
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "jj!1")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (expand
                                                                                           "bounded_above?")
                                                                                          (("2"
                                                                                            (expand
                                                                                             "upper_bound?")
                                                                                            (("2"
                                                                                              (inst
                                                                                               1
                                                                                               "b!1")
                                                                                              (("2"
                                                                                                (skosimp*)
                                                                                                (("2"
                                                                                                  (typepred
                                                                                                   "s!2")
                                                                                                  (("2"
                                                                                                    (skosimp*)
                                                                                                    (("2"
                                                                                                      (inst
                                                                                                       -4
                                                                                                       "j!1")
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (replace
                                                             -4
                                                             *
                                                             rl)
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (typepred
                                                                 "lub(A(1))")
                                                                (("2"
                                                                  (expand
                                                                   "least_upper_bound?")
                                                                  (("2"
                                                                    (flatten)
                                                                    (("2"
                                                                      (inst
                                                                       -2
                                                                       "b!1")
                                                                      (("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (expand
                                                                           "upper_bound?")
                                                                          (("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (typepred
                                                                               "s!1")
                                                                              (("2"
                                                                                (hide
                                                                                 -4
                                                                                 -5
                                                                                 -6)
                                                                                (("2"
                                                                                  (replace
                                                                                   -4
                                                                                   -
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         -5
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (inst + "1")
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (prop)
                                        (("1"
                                          (expand "nonempty?")
                                          (("1"
                                            (expand "empty?")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (inst -1 "alpha(1)")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst + "1")
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (expand "bounded_below?")
                                          (("2"
                                            (expand "lower_bound?")
                                            (("2"
                                              (inst 1 "a!1")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (typepred "s!1")
                                                  (("2"
                                                    (skosimp*)
                                                    (("2"
                                                      (replace
                                                       -2
                                                       -1
                                                       rl)
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (hide -2)
                                                          (("2"
                                                            (replace
                                                             -2
                                                             -1
                                                             rl)
                                                            (("2"
                                                              (hide -2)
                                                              (("2"
                                                                (assert)
                                                                (("2"
                                                                  (typepred
                                                                   "lub({xx: real | EXISTS (j: posnat): j >= jj!1 AND xx = XX!1(j)})")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (replace
                                                                         -3
                                                                         *
                                                                         rl)
                                                                        (("1"
                                                                          (hide
                                                                           -3)
                                                                          (("1"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "XX!1(jj!1)")
                                                                                (("1"
                                                                                  (inst
                                                                                   -3
                                                                                   "jj!1")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (inst
                                                                                   +
                                                                                   "jj!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (prop)
                                                                    (("1"
                                                                      (expand
                                                                       "nonempty?")
                                                                      (("1"
                                                                        (expand
                                                                         "empty?")
                                                                        (("1"
                                                                          (expand
                                                                           "member")
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "XX!1(jj!1)")
                                                                            (("1"
                                                                              (inst
                                                                               +
                                                                               "jj!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (expand
                                                                       "bounded_above?")
                                                                      (("2"
                                                                        (expand
                                                                         "upper_bound?")
                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (typepred
                                                                               "s!2")
                                                                              (("2"
                                                                                (skosimp*)
                                                                                (("2"
                                                                                  (inst
                                                                                   -4
                                                                                   "j!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (skosimp*)
                                      (("2"
                                        (prop)
                                        (("1"
                                          (expand "nonempty?")
                                          (("1"
                                            (expand "empty?")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (replace -2 -1 rl)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst
                                                     -1
                                                     "XX!1(kk!1)")
                                                    (("1"
                                                      (assert)
                                                      (("1"
                                                        (inst + "kk!1")
                                                        (("1"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (expand "bounded_above?")
                                          (("2"
                                            (expand "upper_bound?")
                                            (("2"
                                              (inst + "b!1")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (typepred "s!1")
                                                  (("2"
                                                    (replace -2 -1 rl)
                                                    (("2"
                                                      (hide -2)
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (skosimp*)
                                                          (("2"
                                                            (inst
                                                             -3
                                                             "j!1")
                                                            (("2"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (skosimp*)
                              (("2"
                                (inst -1 "n!1")
                                (("2"
                                  (skosimp*)
                                  (("2"
                                    (inst + "x!1" "y!1")
                                    (("2"
                                      (assert)
                                      (("2" (postpone) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (skosimp*)
                            (("2" (lemma "connected_domain")
                              (("2"
                                (inst -1 "a!1" "b!1" "y!1")
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil)
                           ("3" (skosimp*)
                            (("3" (lemma "connected_domain")
                              (("3"
                                (inst -1 "a!1" "b!1" "x!1")
                                (("3" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (inst + "epsi!1")
                    (("2" (skosimp*)
                      (("2" (inst 2 "N!1")
                        (("2" (skosimp*)
                          (("2" (inst + "x!1" "y!1")
                            (("2" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   nil shostak)
  (unif_cont_interval-4 nil 3399972710
   (";;; Proof unif_cont_interval-4 for formula unif_cont_fun.unif_cont_interval"
    (skosimp*)
    ((";;; Proof unif_cont_interval-4 for formula unif_cont_fun.unif_cont_interval"
      (assert)
      ((";;; Proof unif_cont_interval-4 for formula unif_cont_fun.unif_cont_interval"
        (flatten)
        ((";;; Proof unif_cont_interval-4 for formula unif_cont_fun.unif_cont_interval"
          (expand "uniformly_continuous?")
          ((";;; Proof unif_cont_interval-4 for formula unif_cont_fun.unif_cont_interval"
            (skosimp*)
            ((";;; Proof unif_cont_interval-4 for formula unif_cont_fun.unif_cont_interval"
              (case "  EXISTS (N: posnat):
                                                                                                                        FORALL (x,
                                                                                                                                y:
                                                                                                                                  (extend[real, T, bool, FALSE]
                                                                                                                                       ({xx: T | a!1 <= xx AND xx <= b!1}))):
                                                                                                                          abs(x - y) < 1/N IMPLIES abs(f!1(x) - f!1(y)) < epsi!1")
              (("1" (skosimp*) (("1" (inst + "1/N!1"nil)))
               ("2" (hide 2)
                (("2"
                  (case "EXISTS (eps: posreal): FORALL (N: posnat):
                                                                                                                                                                          EXISTS (x,
                                                                                                                                                                                  y:
                                                                                                                                                                                    (extend[real, T, bool, FALSE]
                                                                                                                                                                                         ({xx: T | a!1 <= xx AND xx <= b!1}))):
                                                                                                                                                                            abs(x - y) < 1/N AND abs(f!1(x) - f!1(y)) >= eps")
                  (("1" (skosimp*)
                    (("1" (hide 1)
                      (("1" (lemma "getem_scaf4")
                        (("1"
                          (inst -1
                           "(LAMBDA (x,y: real,n:posnat): abs(x - y) < 1 / n AND a!1 <= x AND x <= b!1 AND a!1 <= y AND y <= b!1 AND abs(f!1(x) - f!1(y)) >= eps!1)")
                          (("1" (split -1)
                            (("1" (hide -2)
                              (("1"
                                (skosimp*)
                                (("1"
                                  (name
                                   "A"
                                   "(LAMBDA (kk: posnat): {xx: real | EXISTS (j: posnat): j >= kk AND xx = XX!1(j)})")
                                  (("1"
                                    (name
                                     "alpha"
                                     "(LAMBDA (kk: posnat): lub(A(kk)))")
                                    (("1"
                                      (name
                                       "CC"
                                       "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                      (("1"
                                        (case
                                         "a!1 <= CC AND CC <= b!1")
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (expand "continuous?")
                                            (("1"
                                              (inst -8 "CC")
                                              (("1"
                                                (expand "convergence")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst -9 "eps!1/2")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (expand
                                                         "extend")
                                                        (("1"
                                                          (case
                                                           "EXISTS (kk: posnat): CC <= alpha(kk) AND alpha(kk) < CC + delta!1/2 AND 1/kk < delta!1/2")
                                                          (("1"
                                                            (skosimp*)
                                                            (("1"
                                                              (case
                                                               "EXISTS (nn: posnat): alpha(kk!1) - delta!1/2 < XX!1(nn) AND XX!1(nn) <= alpha(kk!1) AND nn >= kk!1")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   -12
                                                                   "nn!1")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "1/nn!1 < delta!1/2")
                                                                      (("1"
                                                                        (case
                                                                         "CC - delta!1/2 <= XX!1(nn!1) AND XX!1(nn!1) <= CC + delta!1/2")
                                                                        (("1"
                                                                          (case
                                                                           "CC - delta!1 < YY!1(nn!1) AND YY!1(nn!1) < CC + delta!1")
                                                                          (("1"
                                                                            (flatten)
                                                                            (("1"
                                                                              (lemma
                                                                               "triangle")
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "f!1(XX!1(nn!1)) -f!1(CC)"
                                                                                 "f!1(CC) - f!1(YY!1(nn!1))")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (inst-cp
                                                                                     -26
                                                                                     "XX!1(nn!1)")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -26
                                                                                       "YY!1(nn!1)")
                                                                                      (("1"
                                                                                        (split
                                                                                         -26)
                                                                                        (("1"
                                                                                          (split
                                                                                           -27)
                                                                                          (("1"
                                                                                            (hide
                                                                                             -4
                                                                                             -5
                                                                                             -7
                                                                                             -8
                                                                                             -9
                                                                                             -11)
                                                                                            (("1"
                                                                                              (case-replace
                                                                                               "abs(f!1(CC) - f!1(YY!1(nn!1))) = abs(f!1(YY!1(nn!1))-f!1(CC))")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide-all-but
                                                                                                 1)
                                                                                                (("2"
                                                                                                  (grind)
                                                                                                  nil)))))))
                                                                                           ("2"
                                                                                            (propax)
                                                                                            nil)
                                                                                           ("3"
                                                                                            (propax)
                                                                                            nil)
                                                                                           ("4"
                                                                                            (hide-all-but
                                                                                             (-5
                                                                                              -6
                                                                                              1))
                                                                                            (("4"
                                                                                              (name-replace
                                                                                               "xxnn"
                                                                                               "XX!1(nn!1)")
                                                                                              (("4"
                                                                                                (grind)
                                                                                                nil)))))))
                                                                                         ("2"
                                                                                          (propax)
                                                                                          nil)
                                                                                         ("3"
                                                                                          (propax)
                                                                                          nil)
                                                                                         ("4"
                                                                                          (hide-all-but
                                                                                           (-2
                                                                                            -3
                                                                                            1))
                                                                                          (("4"
                                                                                            (name-replace
                                                                                             "yynn"
                                                                                             "YY!1(nn!1)")
                                                                                            (("4"
                                                                                              (grind)
                                                                                              nil)))))))))))))
                                                                                 ("2"
                                                                                  (lemma
                                                                                   "connected_domain")
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "a!1"
                                                                                     "b!1"
                                                                                     "CC")
                                                                                    (("2"
                                                                                      (assert)
                                                                                      nil)))))))))))
                                                                           ("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -14
                                                                              1))
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (grind)
                                                                                nil)))))))
                                                                         ("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -3
                                                                              -5
                                                                              -6
                                                                              -7
                                                                              -8
                                                                              -9
                                                                              1))
                                                                            (("2"
                                                                              (name-replace
                                                                               "xxnn"
                                                                               "XX!1(nn!1)")
                                                                              (("2"
                                                                                (assert)
                                                                                nil)))))))))
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-3
                                                                              -6
                                                                              1))
                                                                            (("2"
                                                                              (case
                                                                               "1/nn!1 <= 1/kk!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil)
                                                                               ("2"
                                                                                (hide
                                                                                 -2
                                                                                 2)
                                                                                (("2"
                                                                                  (cross-mult
                                                                                   1)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil)))))))))))))))))))))
                                                               ("2"
                                                                (hide
                                                                 -9
                                                                 -11
                                                                 -12)
                                                                (("2"
                                                                  (typepred
                                                                   "lub(A(kk!1))")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (inst
                                                                         -2
                                                                         "alpha(kk!1)- delta!1 / 2")
                                                                        (("1"
                                                                          (split
                                                                           -2)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                nil)))))
                                                                           ("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -10
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          (("2"
                                                                                            (replace
                                                                                             -2)
                                                                                            (("2"
                                                                                              (hide
                                                                                               -2)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "CC <= XX!1(j!1)")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -10
                                                                                                     *
                                                                                                     rl)
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -
                                                                                                         "XX!1(j!1)")
                                                                                                        nil)))))))
                                                                                                 ("2"
                                                                                                  (inst
                                                                                                   -
                                                                                                   "XX!1(j!1)")
                                                                                                  (("2"
                                                                                                    (assert)
                                                                                                    nil)))))))))))))))))))))))))))))))))
                                                                   ("2"
                                                                    (hide
                                                                     2)
                                                                    (("2"
                                                                      (prop)
                                                                      (("1"
                                                                        (expand
                                                                         "nonempty?")
                                                                        (("1"
                                                                          (expand
                                                                           "empty?")
                                                                          (("1"
                                                                            (expand
                                                                             "member")
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (inst
                                                                                   -1
                                                                                   "XX!1(kk!1)")
                                                                                  (("1"
                                                                                    (inst
                                                                                     +
                                                                                     "kk!1")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      nil)))))))))))))))
                                                                       ("2"
                                                                        (expand
                                                                         "bounded_above?")
                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -9
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (reveal
                                                                                         -1)
                                                                                        (("2"
                                                                                          (inst
                                                                                           -1
                                                                                           "j!1")
                                                                                          (("2"
                                                                                            (assert)
                                                                                            nil)))))))))))))))))))))))))))))))))
                                                           ("2"
                                                            (typepred
                                                             "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                                            (("2"
                                                              (expand
                                                               "greatest_lower_bound?")
                                                              (("2"
                                                                (flatten)
                                                                (("2"
                                                                  (expand
                                                                   "lower_bound?")
                                                                  (("2"
                                                                    (replace
                                                                     -5
                                                                     -)
                                                                    (("2"
                                                                      (inst
                                                                       -2
                                                                       "CC+delta!1/2")
                                                                      (("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (skosimp*)
                                                                          (("2"
                                                                            (typepred
                                                                             "s!1")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (case
                                                                                 "FORALL (ii: posnat): ii >= jj!1 IMPLIES alpha(ii) <= alpha(jj!1)")
                                                                                (("1"
                                                                                  (case
                                                                                   "(EXISTS (jk: posnat): jk >= jj!1 AND 1/jk < delta!1/2)")
                                                                                  (("1"
                                                                                    (skosimp*)
                                                                                    (("1"
                                                                                      (inst
                                                                                       2
                                                                                       "jk!1")
                                                                                      (("1"
                                                                                        (assert)
                                                                                        (("1"
                                                                                          (inst
                                                                                           -3
                                                                                           "jk!1")
                                                                                          (("1"
                                                                                            (assert)
                                                                                            (("1"
                                                                                              (inst
                                                                                               -5
                                                                                               "alpha(jk!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "jk!1")
                                                                                                  nil)))))))))))))))
                                                                                   ("2"
                                                                                    (hide-all-but
                                                                                     1)
                                                                                    (("2"
                                                                                      (lemma
                                                                                       "archimedean")
                                                                                      (("2"
                                                                                        (inst
                                                                                         -1
                                                                                         "delta!1/2")
                                                                                        (("2"
                                                                                          (skosimp*)
                                                                                          (("2"
                                                                                            (inst
                                                                                             +
                                                                                             "max(jj!1,n!1)")
                                                                                            (("2"
                                                                                              (expand
                                                                                               "max")
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (ground)
                                                                                                  (("2"
                                                                                                    (case
                                                                                                     "1/jj!1 <= 1/n!1")
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (cross-mult
                                                                                                       1)
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        nil)))))))))))))))))))))))
                                                                                 ("2"
                                                                                  (hide
                                                                                   -1
                                                                                   -2
                                                                                   -3
                                                                                   -4
                                                                                   -5
                                                                                   -10
                                                                                   -11
                                                                                   2
                                                                                   3)
                                                                                  (("2"
                                                                                    (skosimp*)
                                                                                    (("2"
                                                                                      (replace
                                                                                       -2
                                                                                       *
                                                                                       rl)
                                                                                      (("2"
                                                                                        (assert)
                                                                                        (("2"
                                                                                          (replace
                                                                                           -3
                                                                                           *
                                                                                           rl)
                                                                                          (("2"
                                                                                            (hide
                                                                                             -2
                                                                                             -3)
                                                                                            (("2"
                                                                                              (assert)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "(FORALL (A,B: (bounded_above?)): subset?(A,B) IMPLIES
                                                                                                                                                                                       lub(A) <= lub(B))")
                                                                                                (("1"
                                                                                                  (inst?)
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    (("1"
                                                                                                      (hide
                                                                                                       2)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "subset?")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "member")
                                                                                                          (("1"
                                                                                                            (skosimp*)
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               +
                                                                                                               "j!1")
                                                                                                              (("1"
                                                                                                                (assert)
                                                                                                                nil)))))))))))))
                                                                                                   ("2"
                                                                                                    (hide
                                                                                                     2)
                                                                                                    (("2"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "nonempty?")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "empty?")
                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "member")
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "XX!1(jj!1)")
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "jj!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil)))))))))))
                                                                                                       ("2"
                                                                                                        (expand
                                                                                                         "bounded_above?")
                                                                                                        (("2"
                                                                                                          (inst
                                                                                                           +
                                                                                                           "b!1")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "upper_bound?")
                                                                                                            (("2"
                                                                                                              (skosimp*)
                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "s!2")
                                                                                                                (("2"
                                                                                                                  (skosimp*)
                                                                                                                  (("2"
                                                                                                                    (inst
                                                                                                                     -4
                                                                                                                     "j!1")
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil)))))))))))))))))))
                                                                                                   ("3"
                                                                                                    (hide
                                                                                                     2)
                                                                                                    (("3"
                                                                                                      (prop)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "nonempty?")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "empty?")
                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "member")
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "XX!1(ii!1)")
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "ii!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil)))))))))))
                                                                                                       ("2"
                                                                                                        (expand
                                                                                                         "bounded_above?")
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "upper_bound?")
                                                                                                          (("2"
                                                                                                            (inst
                                                                                                             +
                                                                                                             "b!1")
                                                                                                            (("2"
                                                                                                              (skosimp*)
                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "s!2")
                                                                                                                (("2"
                                                                                                                  (skosimp*)
                                                                                                                  (("2"
                                                                                                                    (inst
                                                                                                                     -4
                                                                                                                     "j!1")
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil)))))))))))))))))))))
                                                                                                 ("2"
                                                                                                  (hide
                                                                                                   2)
                                                                                                  (("2"
                                                                                                    (skosimp*)
                                                                                                    (("2"
                                                                                                      (hide
                                                                                                       -2
                                                                                                       -3
                                                                                                       -4)
                                                                                                      (("2"
                                                                                                        (typepred
                                                                                                         "lub(A!1)")
                                                                                                        (("2"
                                                                                                          (typepred
                                                                                                           "lub(B!1)")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "least_upper_bound?")
                                                                                                            (("2"
                                                                                                              (flatten)
                                                                                                              (("2"
                                                                                                                (inst
                                                                                                                 -4
                                                                                                                 "lub(B!1)")
                                                                                                                (("2"
                                                                                                                  (assert)
                                                                                                                  (("2"
                                                                                                                    (hide
                                                                                                                     2)
                                                                                                                    (("2"
                                                                                                                      (expand
                                                                                                                       "upper_bound?")
                                                                                                                      (("2"
                                                                                                                        (skosimp*)
                                                                                                                        (("2"
                                                                                                                          (typepred
                                                                                                                           "s!2")
                                                                                                                          (("2"
                                                                                                                            (expand
                                                                                                                             "subset?")
                                                                                                                            (("2"
                                                                                                                              (expand
                                                                                                                               "member")
                                                                                                                              (("2"
                                                                                                                                (inst
                                                                                                                                 -5
                                                                                                                                 "s!2")
                                                                                                                                (("2"
                                                                                                                                  (inst
                                                                                                                                   -2
                                                                                                                                   "s!2")
                                                                                                                                  (("2"
                                                                                                                                    (assert)
                                                                                                                                    nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
                                               ("2"
                                                (expand "extend")
                                                (("2"
                                                  (ground)
                                                  (("2"
                                                    (lemma
                                                     "connected_domain")
                                                    (("2"
                                                      (inst
                                                       -1
                                                       "a!1"
                                                       "b!1"
                                                       "CC")
                                                      (("2"
                                                        (assert)
                                                        nil)))))))))))))))
                                         ("2"
                                          (assert)
                                          (("2"
                                            (hide -6)
                                            (("2"
                                              (typepred
                                               "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                              (("2"
                                                (expand
                                                 "greatest_lower_bound?")
                                                (("2"
                                                  (flatten)
                                                  (("2"
                                                    (expand
                                                     "lower_bound?")
                                                    (("2"
                                                      (inst
                                                       -1
                                                       "alpha(1)")
                                                      (("1"
                                                        (replace -3)
                                                        (("1"
                                                          (case
                                                           "alpha(1) <= b!1")
                                                          (("1"
                                                            (assert)
                                                            (("1"
                                                              (inst
                                                               -3
                                                               "a!1")
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (skosimp*)
                                                                  (("1"
                                                                    (typepred
                                                                     "s!1")
                                                                    (("1"
                                                                      (skosimp*)
                                                                      (("1"
                                                                        (replace
                                                                         -5
                                                                         *
                                                                         rl)
                                                                        (("1"
                                                                          (assert)
                                                                          (("1"
                                                                            (hide
                                                                             -5)
                                                                            (("1"
                                                                              (replace
                                                                               -5
                                                                               *
                                                                               rl)
                                                                              (("1"
                                                                                (hide
                                                                                 -5)
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (hide
                                                                                     -2
                                                                                     -3
                                                                                     -4)
                                                                                    (("1"
                                                                                      (typepred
                                                                                       "lub({xx: real | EXISTS (j: posnat): j >= jj!1 AND xx = XX!1(j)})")
                                                                                      (("1"
                                                                                        (expand
                                                                                         "least_upper_bound?")
                                                                                        (("1"
                                                                                          (flatten)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "upper_bound?")
                                                                                            (("1"
                                                                                              (inst
                                                                                               -1
                                                                                               "XX!1(jj!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -4
                                                                                                   "jj!1")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil)))))
                                                                                               ("2"
                                                                                                (inst
                                                                                                 +
                                                                                                 "jj!1")
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  nil)))))))))))
                                                                                       ("2"
                                                                                        (prop)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "nonempty?")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "empty?")
                                                                                            (("1"
                                                                                              (expand
                                                                                               "member")
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -1
                                                                                                 "XX!1(jj!1)")
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "jj!1")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil)))))))))))
                                                                                         ("2"
                                                                                          (expand
                                                                                           "bounded_above?")
                                                                                          (("2"
                                                                                            (expand
                                                                                             "upper_bound?")
                                                                                            (("2"
                                                                                              (inst
                                                                                               1
                                                                                               "b!1")
                                                                                              (("2"
                                                                                                (skosimp*)
                                                                                                (("2"
                                                                                                  (typepred
                                                                                                   "s!2")
                                                                                                  (("2"
                                                                                                    (skosimp*)
                                                                                                    (("2"
                                                                                                      (inst
                                                                                                       -4
                                                                                                       "j!1")
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        nil)))))))))))))))))))))))))))))))))))))))))))))
                                                           ("2"
                                                            (replace
                                                             -4
                                                             *
                                                             rl)
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (typepred
                                                                 "lub(A(1))")
                                                                (("2"
                                                                  (expand
                                                                   "least_upper_bound?")
                                                                  (("2"
                                                                    (flatten)
                                                                    (("2"
                                                                      (inst
                                                                       -2
                                                                       "b!1")
                                                                      (("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (expand
                                                                           "upper_bound?")
                                                                          (("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (typepred
                                                                               "s!1")
                                                                              (("2"
                                                                                (hide
                                                                                 -4
                                                                                 -5
                                                                                 -6)
                                                                                (("2"
                                                                                  (replace
                                                                                   -4
                                                                                   -
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         -5
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil)))))))))))))))))))))))))))))))))))
                                                       ("2"
                                                        (inst + "1")
                                                        nil)))))))))))))))))
                                       ("2"
                                        (prop)
                                        (("1"
                                          (expand "nonempty?")
                                          (("1"
                                            (expand "empty?")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (inst -1 "alpha(1)")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst + "1")
                                                    nil)))))))))))
                                         ("2"
                                          (expand "bounded_below?")
                                          (("2"
                                            (expand "lower_bound?")
                                            (("2"
                                              (inst 1 "a!1")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (typepred "s!1")
                                                  (("2"
                                                    (skosimp*)
                                                    (("2"
                                                      (replace
                                                       -2
                                                       -1
                                                       rl)
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (hide -2)
                                                          (("2"
                                                            (replace
                                                             -2
                                                             -1
                                                             rl)
                                                            (("2"
                                                              (hide -2)
                                                              (("2"
                                                                (assert)
                                                                (("2"
                                                                  (typepred
                                                                   "lub({xx: real | EXISTS (j: posnat): j >= jj!1 AND xx = XX!1(j)})")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (replace
                                                                         -3
                                                                         *
                                                                         rl)
                                                                        (("1"
                                                                          (hide
                                                                           -3)
                                                                          (("1"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "XX!1(jj!1)")
                                                                                (("1"
                                                                                  (inst
                                                                                   -3
                                                                                   "jj!1")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    nil)))
                                                                                 ("2"
                                                                                  (inst
                                                                                   +
                                                                                   "jj!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil)))))))))))))))))
                                                                   ("2"
                                                                    (prop)
                                                                    (("1"
                                                                      (expand
                                                                       "nonempty?")
                                                                      (("1"
                                                                        (expand
                                                                         "empty?")
                                                                        (("1"
                                                                          (expand
                                                                           "member")
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "XX!1(jj!1)")
                                                                            (("1"
                                                                              (inst
                                                                               +
                                                                               "jj!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil)))))))))))
                                                                     ("2"
                                                                      (expand
                                                                       "bounded_above?")
                                                                      (("2"
                                                                        (expand
                                                                         "upper_bound?")
                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (typepred
                                                                               "s!2")
                                                                              (("2"
                                                                                (skosimp*)
                                                                                (("2"
                                                                                  (inst
                                                                                   -4
                                                                                   "j!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil)))))))))))))))))))))))))))))))))))))))))))))))
                                     ("2"
                                      (skosimp*)
                                      (("2"
                                        (prop)
                                        (("1"
                                          (expand "nonempty?")
                                          (("1"
                                            (expand "empty?")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (replace -2 -1 rl)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst
                                                     -1
                                                     "XX!1(kk!1)")
                                                    (("1"
                                                      (assert)
                                                      (("1"
                                                        (inst + "kk!1")
                                                        (("1"
                                                          (assert)
                                                          nil)))))))))))))))))
                                         ("2"
                                          (expand "bounded_above?")
                                          (("2"
                                            (expand "upper_bound?")
                                            (("2"
                                              (inst + "b!1")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (typepred "s!1")
                                                  (("2"
                                                    (replace -2 -1 rl)
                                                    (("2"
                                                      (hide -2)
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (skosimp*)
                                                          (("2"
                                                            (inst
                                                             -3
                                                             "j!1")
                                                            (("2"
                                                              (assert)
                                                              nil)))))))))))))))))))))))))))))))))
                             ("2" (skosimp*)
                              (("2"
                                (inst -1 "n!1")
                                (("2"
                                  (skosimp*)
                                  (("2"
                                    (inst + "x!1" "y!1")
                                    (("2"
                                      (assert)
                                      (("2"
                                        (typepred "x!1")
                                        (("2"
                                          (typepred "y!1")
                                          (("2"
                                            (expand "extend")
                                            (("2"
                                              (ground)
                                              nil)))))))))))))))))))
                           ("2" (skosimp*)
                            (("2" (lemma "connected_domain")
                              (("2"
                                (inst -1 "a!1" "b!1" "y!1")
                                (("2" (assertnil)))))))
                           ("3" (skosimp*)
                            (("3" (lemma "connected_domain")
                              (("3"
                                (inst -1 "a!1" "b!1" "x!1")
                                (("3" (assertnil)))))))))))))))
                   ("2" (inst + "epsi!1")
                    (("2" (skosimp*)
                      (("2" (inst 2 "N!1")
                        (("2" (skosimp*)
                          (("2" (inst + "x!1" "y!1")
                            (("2" (assertnil)))))))))))))))
               ("3" (hide 2)
                (("3" (skosimp*)
                  (("3" (typepred "y!1")
                    (("3" (expand "extend") (("3" (ground) nil)))))))))
               ("4" (hide 2)
                (("4" (skosimp*)
                  (("4" (typepred "x!1")
                    (("4" (expand "extend")
                      (("4" (ground) nil))))))))))))))))))))
    ";;; developed with shostak decision procedures")
   ((convergence const-decl "bool" convergence_functions nil)) nil)
  (unif_cont_interval-3 nil 3324907680
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (expand "uniformly_continuous?")
          (("" (skosimp*)
            ((""
              (case "  EXISTS (N: posnat):
                                                                                                          FORALL (x,
                                                                                                                  y:
                                                                                                                    (extend[real, T, bool, FALSE]
                                                                                                                         ({xx: T | a!1 <= xx AND xx <= b!1}))):
                                                                                                            abs(x - y) < 1/N IMPLIES abs(f!1(x) - f!1(y)) < epsi!1")
              (("1" (skosimp*) (("1" (inst + "1/N!1"nil nil)) nil)
               ("2" (hide 2)
                (("2"
                  (case "EXISTS (eps: posreal): FORALL (N: posnat):
                                                                                                                                                        EXISTS (x,
                                                                                                                                                                y:
                                                                                                                                                                  (extend[real, T, bool, FALSE]
                                                                                                                                                                       ({xx: T | a!1 <= xx AND xx <= b!1}))):
                                                                                                                                                          abs(x - y) < 1/N AND abs(f!1(x) - f!1(y)) >= eps")
                  (("1" (skosimp*)
                    (("1" (hide 1)
                      (("1" (lemma "getem_scaf4")
                        (("1"
                          (inst -1
                           "(LAMBDA (x,y: real,n:posnat): abs(x - y) < 1 / n AND a!1 <= x AND x <= b!1 AND a!1 <= y AND y <= b!1 AND abs(f!1(x) - f!1(y)) >= eps!1)")
                          (("1" (split -1)
                            (("1" (hide -2)
                              (("1"
                                (skosimp*)
                                (("1"
                                  (name
                                   "A"
                                   "(LAMBDA (kk: posnat): {xx: real | EXISTS (j: posnat): j >= kk AND xx = XX!1(j)})")
                                  (("1"
                                    (name
                                     "alpha"
                                     "(LAMBDA (kk: posnat): lub(A(kk)))")
                                    (("1"
                                      (name
                                       "CC"
                                       "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                      (("1"
                                        (case
                                         "a!1 <= CC AND CC <= b!1")
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (expand "continuous?")
                                            (("1"
                                              (inst -8 "CC")
                                              (("1"
                                                (expand "convergence")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst -9 "eps!1/2")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (expand
                                                         "extend")
                                                        (("1"
                                                          (case
                                                           "EXISTS (kk: posnat): CC <= alpha(kk) AND alpha(kk) < CC + delta!1/2 AND 1/kk < delta!1/2")
                                                          (("1"
                                                            (skosimp*)
                                                            (("1"
                                                              (case
                                                               "EXISTS (nn: posnat): alpha(kk!1) - delta!1/2 < XX!1(nn) AND XX!1(nn) <= alpha(kk!1) AND nn >= kk!1")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   -12
                                                                   "nn!1")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "1/nn!1 < delta!1/2")
                                                                      (("1"
                                                                        (case
                                                                         "CC - delta!1/2 <= XX!1(nn!1) AND XX!1(nn!1) <= CC + delta!1/2")
                                                                        (("1"
                                                                          (case
                                                                           "CC - delta!1 < YY!1(nn!1) AND YY!1(nn!1) < CC + delta!1")
                                                                          (("1"
                                                                            (flatten)
                                                                            (("1"
                                                                              (lemma
                                                                               "triangle")
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "f!1(XX!1(nn!1)) -f!1(CC)"
                                                                                 "f!1(CC) - f!1(YY!1(nn!1))")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (inst-cp
                                                                                     -26
                                                                                     "XX!1(nn!1)")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -26
                                                                                       "YY!1(nn!1)")
                                                                                      (("1"
                                                                                        (split
                                                                                         -26)
                                                                                        (("1"
                                                                                          (split
                                                                                           -27)
                                                                                          (("1"
                                                                                            (hide
                                                                                             -4
                                                                                             -5
                                                                                             -7
                                                                                             -8
                                                                                             -9
                                                                                             -11)
                                                                                            (("1"
                                                                                              (case-replace
                                                                                               "abs(f!1(CC) - f!1(YY!1(nn!1))) = abs(f!1(YY!1(nn!1))-f!1(CC))")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                nil
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide-all-but
                                                                                                 1)
                                                                                                (("2"
                                                                                                  (grind)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("3"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("4"
                                                                                            (hide-all-but
                                                                                             (-5
                                                                                              -6
                                                                                              1))
                                                                                            (("4"
                                                                                              (name-replace
                                                                                               "xxnn"
                                                                                               "XX!1(nn!1)")
                                                                                              (("4"
                                                                                                (grind)
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("3"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("4"
                                                                                          (hide-all-but
                                                                                           (-2
                                                                                            -3
                                                                                            1))
                                                                                          (("4"
                                                                                            (name-replace
                                                                                             "yynn"
                                                                                             "YY!1(nn!1)")
                                                                                            (("4"
                                                                                              (grind)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (lemma
                                                                                   "connected_domain")
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "a!1"
                                                                                     "b!1"
                                                                                     "CC")
                                                                                    (("2"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -14
                                                                              1))
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (grind)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -3
                                                                              -5
                                                                              -6
                                                                              -7
                                                                              -8
                                                                              -9
                                                                              1))
                                                                            (("2"
                                                                              (name-replace
                                                                               "xxnn"
                                                                               "XX!1(nn!1)")
                                                                              (("2"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-3
                                                                              -6
                                                                              1))
                                                                            (("2"
                                                                              (case
                                                                               "1/nn!1 <= 1/kk!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("2"
                                                                                (hide
                                                                                 -2
                                                                                 2)
                                                                                (("2"
                                                                                  (cross-mult
                                                                                   1)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide
                                                                 -9
                                                                 -11
                                                                 -12)
                                                                (("2"
                                                                  (typepred
                                                                   "lub(A(kk!1))")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (inst
                                                                         -2
                                                                         "alpha(kk!1)- delta!1 / 2")
                                                                        (("1"
                                                                          (split
                                                                           -2)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -10
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          (("2"
                                                                                            (replace
                                                                                             -2)
                                                                                            (("2"
                                                                                              (hide
                                                                                               -2)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "CC <= XX!1(j!1)")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -10
                                                                                                     *
                                                                                                     rl)
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (inst
                                                                                                         -
                                                                                                         "XX!1(j!1)")
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (inst
                                                                                                   -
                                                                                                   "XX!1(j!1)")
                                                                                                  (("2"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (hide
                                                                     2)
                                                                    (("2"
                                                                      (prop)
                                                                      (("1"
                                                                        (expand
                                                                         "nonempty?")
                                                                        (("1"
                                                                          (expand
                                                                           "empty?")
                                                                          (("1"
                                                                            (expand
                                                                             "member")
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                (("1"
                                                                                  (inst
                                                                                   -1
                                                                                   "XX!1(kk!1)")
                                                                                  (("1"
                                                                                    (inst
                                                                                     +
                                                                                     "kk!1")
                                                                                    (("1"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (expand
                                                                         "bounded_above?")
                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -9
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (reveal
                                                                                         -1)
                                                                                        (("2"
                                                                                          (inst
                                                                                           -1
                                                                                           "j!1")
                                                                                          (("2"
                                                                                            (assert)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (typepred
                                                             "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                                            (("2"
                                                              (expand
                                                               "greatest_lower_bound?")
                                                              (("2"
                                                                (flatten)
                                                                (("2"
                                                                  (expand
                                                                   "lower_bound?")
                                                                  (("2"
                                                                    (replace
                                                                     -5
                                                                     -
                                                                     *rl)
                                                                    (("2"
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                                                                       -2
                                                                       "CC+delta!1/2")
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                                                                        (assert)
                                                                        (("2"
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                                                                            (("2"
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                                                                              (("2"
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                                                                                (("1"
                                                                                  (case
                                                                                   "(EXISTS (jk: posnat): jk >= jj!1 AND 1/jk < delta!1/2)")
                                                                                  (("1"
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                                                                                    (("1"
                                                                                      (inst
                                                                                       2
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                                                                                      (("1"
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                                                                                        (("1"
                                                                                          (inst
                                                                                           -3
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                                                                                          (("1"
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                                                                                            (("1"
                                                                                              (inst
                                                                                               -5
                                                                                               "alpha(jk!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
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                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil)
                                                                                   ("2"
                                                                                    (hide-all-but
                                                                                     1)
                                                                                    (("2"
                                                                                      (lemma
                                                                                       "archimedean")
                                                                                      (("2"
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                                                                                         -1
                                                                                         "delta!1/2")
                                                                                        (("2"
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                                                                                          (("2"
                                                                                            (inst
                                                                                             +
                                                                                             "max(jj!1,n!1)")
                                                                                            (("2"
                                                                                              (expand
                                                                                               "max")
                                                                                              (("2"
                                                                                                (lift-if)
                                                                                                (("2"
                                                                                                  (ground)
                                                                                                  (("2"
                                                                                                    (case
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                                                                                                    (("1"
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                                                                                                      nil
                                                                                                      nil)
                                                                                                     ("2"
                                                                                                      (cross-mult
                                                                                                       1)
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (hide
                                                                                   -1
                                                                                   -2
                                                                                   -3
                                                                                   -4
                                                                                   -5
                                                                                   -10
                                                                                   -11
                                                                                   2
                                                                                   3)
                                                                                  (("2"
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                                                                                    (("2"
                                                                                      (replace
                                                                                       -2
                                                                                       *
                                                                                       rl)
                                                                                      (("2"
                                                                                        (assert)
                                                                                        (("2"
                                                                                          (replace
                                                                                           -3
                                                                                           *
                                                                                           rl)
                                                                                          (("2"
                                                                                            (hide
                                                                                             -2
                                                                                             -3)
                                                                                            (("2"
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                                                                                              (("2"
                                                                                                (case
                                                                                                 "(FORALL (A,B: (bounded_above?)): subset?(A,B) IMPLIES
                                                                                                                                 lub(A) <= lub(B))")
                                                                                                (("1"
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                                                                                                  (("1"
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                                                                                                    (("1"
                                                                                                      (hide
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                                                                                                          (("1"
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                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               +
                                                                                                               "j!1")
                                                                                                              (("1"
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                                                                                                                nil
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil)
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                                                                                                     2)
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                                                                                                         "nonempty?")
                                                                                                        (("1"
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                                                                                                          (("1"
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                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "XX!1(jj!1)")
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "jj!1")
                                                                                                                (("1"
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                                                                                                                  nil))
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                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
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                                                                                                         "bounded_above?")
                                                                                                        (("2"
                                                                                                          (inst
                                                                                                           +
                                                                                                           "b!1")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "upper_bound?")
                                                                                                            (("2"
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                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "s!2")
                                                                                                                (("2"
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                                                                                                                  (("2"
                                                                                                                    (inst
                                                                                                                     -4
                                                                                                                     "j!1")
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil)
                                                                                                   ("3"
                                                                                                    (hide
                                                                                                     2)
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                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "nonempty?")
                                                                                                        (("1"
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                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "member")
                                                                                                            (("1"
                                                                                                              (inst
                                                                                                               -1
                                                                                                               "XX!1(ii!1)")
                                                                                                              (("1"
                                                                                                                (inst
                                                                                                                 +
                                                                                                                 "ii!1")
                                                                                                                (("1"
                                                                                                                  (assert)
                                                                                                                  nil
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil)
                                                                                                       ("2"
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                                                                                                         "bounded_above?")
                                                                                                        (("2"
                                                                                                          (expand
                                                                                                           "upper_bound?")
                                                                                                          (("2"
                                                                                                            (inst
                                                                                                             +
                                                                                                             "b!1")
                                                                                                            (("2"
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                                                                                                              (("2"
                                                                                                                (typepred
                                                                                                                 "s!2")
                                                                                                                (("2"
                                                                                                                  (skosimp*)
                                                                                                                  (("2"
                                                                                                                    (inst
                                                                                                                     -4
                                                                                                                     "j!1")
                                                                                                                    (("2"
                                                                                                                      (assert)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (hide
                                                                                                   2)
                                                                                                  (("2"
                                                                                                    (skosimp*)
                                                                                                    (("2"
                                                                                                      (hide
                                                                                                       -2
                                                                                                       -3
                                                                                                       -4)
                                                                                                      (("2"
                                                                                                        (typepred
                                                                                                         "lub(A!1)")
                                                                                                        (("2"
                                                                                                          (typepred
                                                                                                           "lub(B!1)")
                                                                                                          (("2"
                                                                                                            (expand
                                                                                                             "least_upper_bound?")
                                                                                                            (("2"
                                                                                                              (flatten)
                                                                                                              (("2"
                                                                                                                (inst
                                                                                                                 -4
                                                                                                                 "lub(B!1)")
                                                                                                                (("2"
                                                                                                                  (assert)
                                                                                                                  (("2"
                                                                                                                    (hide
                                                                                                                     2)
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                                                                                                                       "upper_bound?")
                                                                                                                      (("2"
                                                                                                                        (skosimp*)
                                                                                                                        (("2"
                                                                                                                          (typepred
                                                                                                                           "s!2")
                                                                                                                          (("2"
                                                                                                                            (expand
                                                                                                                             "subset?")
                                                                                                                            (("2"
                                                                                                                              (expand
                                                                                                                               "member")
                                                                                                                              (("2"
                                                                                                                                (inst
                                                                                                                                 -5
                                                                                                                                 "s!2")
                                                                                                                                (("2"
                                                                                                                                  (inst
                                                                                                                                   -2
                                                                                                                                   "s!2")
                                                                                                                                  (("2"
                                                                                                                                    (assert)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (expand "extend")
                                                (("2"
                                                  (ground)
                                                  (("2"
                                                    (lemma
                                                     "connected_domain")
                                                    (("2"
                                                      (inst
                                                       -1
                                                       "a!1"
                                                       "b!1"
                                                       "CC")
                                                      (("2"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (assert)
                                          (("2"
                                            (hide -6)
                                            (("2"
                                              (typepred
                                               "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                              (("2"
                                                (expand
                                                 "greatest_lower_bound?")
                                                (("2"
                                                  (flatten)
                                                  (("2"
                                                    (expand
                                                     "lower_bound?")
                                                    (("2"
                                                      (inst
                                                       -1
                                                       "alpha(1)")
                                                      (("1"
                                                        (replace -3)
                                                        (("1"
                                                          (case
                                                           "alpha(1) <= b!1")
                                                          (("1"
                                                            (assert)
                                                            (("1"
                                                              (inst
                                                               -3
                                                               "a!1")
                                                              (("1"
                                                                (assert)
                                                                (("1"
                                                                  (skosimp*)
                                                                  (("1"
                                                                    (typepred
                                                                     "s!1")
                                                                    (("1"
                                                                      (skosimp*)
                                                                      (("1"
                                                                        (replace
                                                                         -5
                                                                         *
                                                                         rl)
                                                                        (("1"
                                                                          (assert)
                                                                          (("1"
                                                                            (hide
                                                                             -5)
                                                                            (("1"
                                                                              (replace
                                                                               -5
                                                                               *
                                                                               rl)
                                                                              (("1"
                                                                                (hide
                                                                                 -5)
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (hide
                                                                                     -2
                                                                                     -3
                                                                                     -4)
                                                                                    (("1"
                                                                                      (typepred
                                                                                       "lub({xx: real | EXISTS (j: posnat): j >= jj!1 AND xx = XX!1(j)})")
                                                                                      (("1"
                                                                                        (expand
                                                                                         "least_upper_bound?")
                                                                                        (("1"
                                                                                          (flatten)
                                                                                          (("1"
                                                                                            (expand
                                                                                             "upper_bound?")
                                                                                            (("1"
                                                                                              (inst
                                                                                               -1
                                                                                               "XX!1(jj!1)")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   -4
                                                                                                   "jj!1")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil)
                                                                                               ("2"
                                                                                                (inst
                                                                                                 +
                                                                                                 "jj!1")
                                                                                                (("2"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil)
                                                                                       ("2"
                                                                                        (prop)
                                                                                        (("1"
                                                                                          (expand
                                                                                           "nonempty?")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "empty?")
                                                                                            (("1"
                                                                                              (expand
                                                                                               "member")
                                                                                              (("1"
                                                                                                (inst
                                                                                                 -1
                                                                                                 "XX!1(jj!1)")
                                                                                                (("1"
                                                                                                  (inst
                                                                                                   +
                                                                                                   "jj!1")
                                                                                                  (("1"
                                                                                                    (assert)
                                                                                                    nil
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (expand
                                                                                           "bounded_above?")
                                                                                          (("2"
                                                                                            (expand
                                                                                             "upper_bound?")
                                                                                            (("2"
                                                                                              (inst
                                                                                               1
                                                                                               "b!1")
                                                                                              (("2"
                                                                                                (skosimp*)
                                                                                                (("2"
                                                                                                  (typepred
                                                                                                   "s!2")
                                                                                                  (("2"
                                                                                                    (skosimp*)
                                                                                                    (("2"
                                                                                                      (inst
                                                                                                       -4
                                                                                                       "j!1")
                                                                                                      (("2"
                                                                                                        (assert)
                                                                                                        nil
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil)
                                                           ("2"
                                                            (replace
                                                             -4
                                                             *
                                                             rl)
                                                            (("2"
                                                              (assert)
                                                              (("2"
                                                                (typepred
                                                                 "lub(A(1))")
                                                                (("2"
                                                                  (expand
                                                                   "least_upper_bound?")
                                                                  (("2"
                                                                    (flatten)
                                                                    (("2"
                                                                      (inst
                                                                       -2
                                                                       "b!1")
                                                                      (("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (expand
                                                                           "upper_bound?")
                                                                          (("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (typepred
                                                                               "s!1")
                                                                              (("2"
                                                                                (hide
                                                                                 -4
                                                                                 -5
                                                                                 -6)
                                                                                (("2"
                                                                                  (replace
                                                                                   -4
                                                                                   -
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         -5
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil)
                                                       ("2"
                                                        (inst + "1")
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (prop)
                                        (("1"
                                          (expand "nonempty?")
                                          (("1"
                                            (expand "empty?")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (inst -1 "alpha(1)")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst + "1")
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (expand "bounded_below?")
                                          (("2"
                                            (expand "lower_bound?")
                                            (("2"
                                              (inst 1 "a!1")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (typepred "s!1")
                                                  (("2"
                                                    (skosimp*)
                                                    (("2"
                                                      (replace
                                                       -2
                                                       -1
                                                       rl)
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (hide -2)
                                                          (("2"
                                                            (replace
                                                             -2
                                                             -1
                                                             rl)
                                                            (("2"
                                                              (hide -2)
                                                              (("2"
                                                                (assert)
                                                                (("2"
                                                                  (typepred
                                                                   "lub({xx: real | EXISTS (j: posnat): j >= jj!1 AND xx = XX!1(j)})")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (replace
                                                                         -3
                                                                         *
                                                                         rl)
                                                                        (("1"
                                                                          (hide
                                                                           -3)
                                                                          (("1"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "XX!1(jj!1)")
                                                                                (("1"
                                                                                  (inst
                                                                                   -3
                                                                                   "jj!1")
                                                                                  (("1"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (inst
                                                                                   +
                                                                                   "jj!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil)
                                                                   ("2"
                                                                    (prop)
                                                                    (("1"
                                                                      (expand
                                                                       "nonempty?")
                                                                      (("1"
                                                                        (expand
                                                                         "empty?")
                                                                        (("1"
                                                                          (expand
                                                                           "member")
                                                                          (("1"
                                                                            (inst
                                                                             -1
                                                                             "XX!1(jj!1)")
                                                                            (("1"
                                                                              (inst
                                                                               +
                                                                               "jj!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (expand
                                                                       "bounded_above?")
                                                                      (("2"
                                                                        (expand
                                                                         "upper_bound?")
                                                                        (("2"
                                                                          (inst
                                                                           +
                                                                           "b!1")
                                                                          (("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (typepred
                                                                               "s!2")
                                                                              (("2"
                                                                                (skosimp*)
                                                                                (("2"
                                                                                  (inst
                                                                                   -4
                                                                                   "j!1")
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil)
                                     ("2"
                                      (skosimp*)
                                      (("2"
                                        (prop)
                                        (("1"
                                          (expand "nonempty?")
                                          (("1"
                                            (expand "empty?")
                                            (("1"
                                              (expand "member")
                                              (("1"
                                                (replace -2 -1 rl)
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (inst
                                                     -1
                                                     "XX!1(kk!1)")
                                                    (("1"
                                                      (assert)
                                                      (("1"
                                                        (inst + "kk!1")
                                                        (("1"
                                                          (assert)
                                                          nil
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (expand "bounded_above?")
                                          (("2"
                                            (expand "upper_bound?")
                                            (("2"
                                              (inst + "b!1")
                                              (("2"
                                                (skosimp*)
                                                (("2"
                                                  (typepred "s!1")
                                                  (("2"
                                                    (replace -2 -1 rl)
                                                    (("2"
                                                      (hide -2)
                                                      (("2"
                                                        (assert)
                                                        (("2"
                                                          (skosimp*)
                                                          (("2"
                                                            (inst
                                                             -3
                                                             "j!1")
                                                            (("2"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil)
                             ("2" (skosimp*)
                              (("2"
                                (inst -1 "n!1")
                                (("2"
                                  (skosimp*)
                                  (("2"
                                    (inst + "x!1" "y!1")
                                    (("2"
                                      (assert)
                                      (("2"
                                        (typepred "x!1")
                                        (("2"
                                          (typepred "y!1")
                                          (("2"
                                            (expand "extend")
                                            (("2" (ground) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("2" (skosimp*)
                            (("2" (lemma "connected_domain")
                              (("2"
                                (inst -1 "a!1" "b!1" "y!1")
                                (("2" (assertnil nil))
                                nil))
                              nil))
                            nil)
                           ("3" (skosimp*)
                            (("3" (lemma "connected_domain")
                              (("3"
                                (inst -1 "a!1" "b!1" "x!1")
                                (("3" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (inst + "epsi!1")
                    (("2" (skosimp*)
                      (("2" (inst 2 "N!1")
                        (("2" (skosimp*)
                          (("2" (inst + "x!1" "y!1")
                            (("2" (assertnil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("3" (hide 2)
                (("3" (skosimp*)
                  (("3" (typepred "y!1")
                    (("3" (expand "extend") (("3" (ground) nil nil))
                      nil))
                    nil))
                  nil))
                nil)
               ("4" (hide 2)
                (("4" (skosimp*)
                  (("4" (typepred "x!1")
                    (("4" (expand "extend") (("4" (ground) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((convergence const-decl "bool" convergence_functions nil)) nil)
  (unif_cont_interval-2 nil 3302349666
   ("" (skosimp*)
    (("" (assert)
      (("" (flatten)
        (("" (expand "uniformly_continuous?")
          (("" (skosimp*)
            ((""
              (case "  EXISTS (N: posnat):
                                                                                                   FORALL (x,
                                                                                                           y:
                                                                                                             (extend[real, T, bool, FALSE]
                                                                                                                  ({xx: T | a!1 <= xx AND xx <= b!1}))):
                                                                                                     abs(x - y) < 1/N IMPLIES abs(f!1(x) - f!1(y)) < epsi!1")
              (("1" (skosimp*) (("1" (inst + "1/N!1"nil nil)) nil)
               ("2" (hide 2)
                (("2"
                  (case "EXISTS (eps: posreal): FORALL (N: posnat):
                                                                                                                                               EXISTS (x,
                                                                                                                                                       y:
                                                                                                                                                         (extend[real, T, bool, FALSE]
                                                                                                                                                              ({xx: T | a!1 <= xx AND xx <= b!1}))):
                                                                                                                                                 abs(x - y) < 1/N AND abs(f!1(x) - f!1(y)) >= eps")
                  (("1" (skosimp*)
                    (("1" (hide 1)
                      (("1" (lemma "getem_prep4")
                        (("1"
                          (inst -1
                           "(LAMBDA (x,y: real,n:posnat): abs(x - y) < 1 / n AND a!1 <= x AND x <= b!1 AND a!1 <= y AND y <= b!1 AND abs(f!1(x) - f!1(y)) >= eps!1)")
                          (("1" (split -1)
                            (("1" (hide -2)
                              (("1"
                                (skosimp*)
                                (("1"
                                  (name
                                   "A"
                                   "(LAMBDA (kk: posnat): {xx: real | EXISTS (j: posnat): j >= kk AND xx = XX!1(j)})")
                                  (("1"
                                    (name
                                     "alpha"
                                     "(LAMBDA (kk: posnat): lub(A(kk)))")
                                    (("1"
                                      (name
                                       "CC"
                                       "glb({alphs: real | EXISTS (jj: posnat): alphs = alpha(jj)})")
                                      (("1"
                                        (case
                                         "a!1 <= CC AND CC <= b!1")
                                        (("1"
                                          (flatten)
                                          (("1"
                                            (expand "continuous?")
                                            (("1"
                                              (inst -8 "CC")
                                              (("1"
                                                (expand "convergence")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst -9 "eps!1/2")
                                                    (("1"
                                                      (skosimp*)
                                                      (("1"
                                                        (expand
                                                         "extend")
                                                        (("1"
                                                          (case
                                                           "EXISTS (kk: posnat): CC <= alpha(kk) AND alpha(kk) < CC + delta!1/2 AND 1/kk < delta!1/2")
                                                          (("1"
                                                            (skosimp*)
                                                            (("1"
                                                              (case
                                                               "EXISTS (nn: posnat): alpha(kk!1) - delta!1/2 < XX!1(nn) AND XX!1(nn) <= alpha(kk!1) AND nn >= kk!1")
                                                              (("1"
                                                                (skosimp*)
                                                                (("1"
                                                                  (inst
                                                                   -12
                                                                   "nn!1")
                                                                  (("1"
                                                                    (flatten)
                                                                    (("1"
                                                                      (case
                                                                       "1/nn!1 < delta!1/2")
                                                                      (("1"
                                                                        (case
                                                                         "CC - delta!1/2 <= XX!1(nn!1) AND XX!1(nn!1) <= CC + delta!1/2")
                                                                        (("1"
                                                                          (case
                                                                           "CC - delta!1 < YY!1(nn!1) AND YY!1(nn!1) < CC + delta!1")
                                                                          (("1"
                                                                            (flatten)
                                                                            (("1"
                                                                              (lemma
                                                                               "triangle")
                                                                              (("1"
                                                                                (inst
                                                                                 -1
                                                                                 "f!1(XX!1(nn!1)) -f!1(CC)"
                                                                                 "f!1(CC) - f!1(YY!1(nn!1))")
                                                                                (("1"
                                                                                  (assert)
                                                                                  (("1"
                                                                                    (inst-cp
                                                                                     -26
                                                                                     "XX!1(nn!1)")
                                                                                    (("1"
                                                                                      (inst
                                                                                       -26
                                                                                       "YY!1(nn!1)")
                                                                                      (("1"
                                                                                        (split
                                                                                         -26)
                                                                                        (("1"
                                                                                          (split
                                                                                           -27)
                                                                                          (("1"
                                                                                            (hide
                                                                                             -4
                                                                                             -5
                                                                                             -7
                                                                                             -8
                                                                                             -9
                                                                                             -11)
                                                                                            (("1"
                                                                                              (case-replace
                                                                                               "abs(f!1(CC) - f!1(YY!1(nn!1))) = abs(f!1(YY!1(nn!1))-f!1(CC))")
                                                                                              (("1"
                                                                                                (assert)
                                                                                                nil
                                                                                                nil)
                                                                                               ("2"
                                                                                                (hide-all-but
                                                                                                 1)
                                                                                                (("2"
                                                                                                  (grind)
                                                                                                  nil
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("3"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("4"
                                                                                            (hide-all-but
                                                                                             (-5
                                                                                              -6
                                                                                              1))
                                                                                            (("4"
                                                                                              (name-replace
                                                                                               "xxnn"
                                                                                               "XX!1(nn!1)")
                                                                                              (("4"
                                                                                                (grind)
                                                                                                nil
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil)
                                                                                         ("2"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("3"
                                                                                          (propax)
                                                                                          nil
                                                                                          nil)
                                                                                         ("4"
                                                                                          (hide-all-but
                                                                                           (-2
                                                                                            -3
                                                                                            1))
                                                                                          (("4"
                                                                                            (name-replace
                                                                                             "yynn"
                                                                                             "YY!1(nn!1)")
                                                                                            (("4"
                                                                                              (grind)
                                                                                              nil
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil)
                                                                                 ("2"
                                                                                  (lemma
                                                                                   "connected_domain")
                                                                                  (("2"
                                                                                    (inst
                                                                                     -
                                                                                     "a!1"
                                                                                     "b!1"
                                                                                     "CC")
                                                                                    (("2"
                                                                                      (assert)
                                                                                      nil
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -14
                                                                              1))
                                                                            (("2"
                                                                              (flatten)
                                                                              (("2"
                                                                                (grind)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-1
                                                                              -2
                                                                              -3
                                                                              -5
                                                                              -6
                                                                              -7
                                                                              -8
                                                                              -9
                                                                              1))
                                                                            (("2"
                                                                              (name-replace
                                                                               "xxnn"
                                                                               "XX!1(nn!1)")
                                                                              (("2"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil)
                                                                       ("2"
                                                                        (assert)
                                                                        (("2"
                                                                          (assert)
                                                                          (("2"
                                                                            (hide-all-but
                                                                             (-3
                                                                              -6
                                                                              1))
                                                                            (("2"
                                                                              (case
                                                                               "1/nn!1 <= 1/kk!1")
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil)
                                                                               ("2"
                                                                                (hide
                                                                                 -2
                                                                                 2)
                                                                                (("2"
                                                                                  (cross-mult
                                                                                   1)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide
                                                                 -9
                                                                 -11
                                                                 -12)
                                                                (("2"
                                                                  (typepred
                                                                   "lub(A(kk!1))")
                                                                  (("1"
                                                                    (expand
                                                                     "least_upper_bound?")
                                                                    (("1"
                                                                      (flatten)
                                                                      (("1"
                                                                        (inst
                                                                         -2
                                                                         "alpha(kk!1)- delta!1 / 2")
                                                                        (("1"
                                                                          (split
                                                                           -2)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (replace
                                                                               -9
                                                                               -1
                                                                               rl)
                                                                              (("1"
                                                                                (assert)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (expand
                                                                             "upper_bound?")
                                                                            (("2"
                                                                              (skosimp*)
                                                                              (("2"
                                                                                (typepred
                                                                                 "s!1")
                                                                                (("2"
                                                                                  (replace
                                                                                   -10
                                                                                   -1
                                                                                   rl)
                                                                                  (("2"
                                                                                    (assert)
                                                                                    (("2"
                                                                                      (skosimp*)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "j!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          (("2"
                                                                                            (replace
                                                                                             -2)
                                                                                            (("2"
                                                                                              (hide
                                                                                               -2)
                                                                                              (("2"
                                                                                                (case
                                                                                                 "CC <= XX!1(j!1)")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -10
--> --------------------

--> maximum size reached

--> --------------------

Messung V0.5 in Prozent
C=100 H=100 G=100

¤ Dauer der Verarbeitung: 0.726 Sekunden  (vorverarbeitet am  2026-04-27) ¤

*© Formatika GbR, Deutschland






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