Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/PVS/lnexp/   (Beweissystem der NASA Version 6.0.9©)  Datei vom 28.9.2014 mit Größe 535 kB image not shown  

Quelle  ln_exp_ineq.prf

  Sprache: Lisp
 

(ln_exp_ineq
 (ln_ineq1_TCC1 0
  (ln_ineq1_TCC1-1 nil 3254127856 ("" (grind) nil nilnil shostak))
 (ln_ineq1_TCC2 0
  (ln_ineq1_TCC2-1 nil 3254127856 ("" (grind) nil nilnil shostak))
 (ln_ineq1 0
  (ln_ineq1-1 nil 3253817629
   ("" (skolem + "x")
    (("" (name "z" "1+x")
      (("" (name "foo" "z-1")
        (("" (typepred "x")
          (("" (replace -4)
            (("" (replace -4 -3 rl)
              (("" (replace -3 (1 -1 -2))
                (("" (replace -4)
                  (("" (replace -3 (-1 -2 1) rl)
                    (("" (hide -3 -4)
                      (("" (simplify -2)
                        (("" (assert)
                          ((""
                            (lemma "both_sides_plus_gt1"
                             ("z" "1" "x" "z-1" "y" "-1"))
                            (("" (replace -1 -3 rl)
                              ((""
                                (simplify -3)
                                ((""
                                  (hide -1)
                                  ((""
                                    (name
                                     "F"
                                     "LAMBDA (x:posreal): x - 1 - ln(x)")
                                    ((""
                                      (name
                                       "G"
                                       "LAMBDA (x:posreal): ln(x) - (x-1)/x")
                                      ((""
                                        (case
                                         "FORALL (x, y: posreal), (z: real): x <= z AND z <= y IMPLIES z >= 0 AND z > 0")
                                        (("1"
                                          (case
                                           "FORALL (x: posreal): EXISTS (y: posreal): x /= y")
                                          (("1"
                                            (lemma "ln_derivable")
                                            (("1"
                                              (flatten -1)
                                              (("1"
                                                (lemma
                                                 "const_derivable_fun[posreal]"
                                                 ("b" "1"))
                                                (("1"
                                                  (lemma
                                                   "identity_derivable_fun[posreal]")
                                                  (("1"
                                                    (lemma
                                                     "diff_derivable_fun[posreal]")
                                                    (("1"
                                                      (inst-cp
                                                       -1
                                                       "I[posreal]"
                                                       "const_fun(1)")
                                                      (("1"
                                                        (inst-cp
                                                         -
                                                         "I[posreal] - const_fun(1)"
                                                         "ln")
                                                        (("1"
                                                          (lemma
                                                           "div_derivable_fun[posreal]"
                                                           ("f"
                                                            "I[posreal]-const_fun(1)"
                                                            "g"
                                                            "I[posreal]"))
                                                          (("1"
                                                            (inst
                                                             -
                                                             "ln"
                                                             "(I[posreal]-const_fun(1))/I[posreal]")
                                                            (("1"
                                                              (lemma
                                                               "deriv_const_fun[posreal]"
                                                               ("b"
                                                                "1"))
                                                              (("1"
                                                                (lemma
                                                                 "deriv_id_fun[posreal]")
                                                                (("1"
                                                                  (lemma
                                                                   "deriv_diff_fun[posreal]")
                                                                  (("1"
                                                                    (replace
                                                                     -10)
                                                                    (("1"
                                                                      (replace
                                                                       -9)
                                                                      (("1"
                                                                        (replace
                                                                         -8)
                                                                        (("1"
                                                                          (replace
                                                                           -7)
                                                                          (("1"
                                                                            (replace
                                                                             -4)
                                                                            (("1"
                                                                              (expand
                                                                               "I")
                                                                              (("1"
                                                                                (expand
                                                                                 "const_fun")
                                                                                (("1"
                                                                                  (expand
                                                                                   "-"
                                                                                   (-4
                                                                                    -5
                                                                                    -6
                                                                                    -7))
                                                                                  (("1"
                                                                                    (expand
                                                                                     "/"
                                                                                     (-4
                                                                                      -5))
                                                                                    (("1"
                                                                                      (inst-cp
                                                                                       -
                                                                                       "LAMBDA (x: posreal): x"
                                                                                       "LAMBDA (x: posreal): 1")
                                                                                      (("1"
                                                                                        (inst-cp
                                                                                         -
                                                                                         "LAMBDA (x:posreal): x - 1"
                                                                                         "ln")
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "deriv_div_fun[posreal]"
                                                                                           ("ff"
                                                                                            "LAMBDA (x:posreal): x-1"
                                                                                            "gg"
                                                                                            "LAMBDA (x:posreal): x"))
                                                                                          (("1"
                                                                                            (inst
                                                                                             -
                                                                                             "ln"
                                                                                             "LAMBDA (x:posreal): (x-1)/x")
                                                                                            (("1"
                                                                                              (expand
                                                                                               "-"
                                                                                               (-1
                                                                                                -2
                                                                                                -3
                                                                                                -4))
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "/")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "*")
                                                                                                  (("1"
                                                                                                    (replace
                                                                                                     -14)
                                                                                                    (("1"
                                                                                                      (replace
                                                                                                       -6)
                                                                                                      (("1"
                                                                                                        (replace
                                                                                                         -5)
                                                                                                        (("1"
                                                                                                          (simplify)
                                                                                                          (("1"
                                                                                                            (replace
                                                                                                             -4)
                                                                                                            (("1"
                                                                                                              (simplify
                                                                                                               -1)
                                                                                                              (("1"
                                                                                                                (replace
                                                                                                                 -1)
                                                                                                                (("1"
                                                                                                                  (simplify
                                                                                                                   -2)
                                                                                                                  (("1"
                                                                                                                    (simplify
                                                                                                                     -3)
                                                                                                                    (("1"
                                                                                                                      (replace
                                                                                                                       -18)
                                                                                                                      (("1"
                                                                                                                        (replace
                                                                                                                         -17)
                                                                                                                        (("1"
                                                                                                                          (hide-all-but
                                                                                                                           (-2
                                                                                                                            -3
                                                                                                                            -8
                                                                                                                            -9
                                                                                                                            -15
                                                                                                                            -16
                                                                                                                            -17
                                                                                                                            -18
                                                                                                                            -19
                                                                                                                            -20
                                                                                                                            1))
                                                                                                                          (("1"
                                                                                                                            (assert)
                                                                                                                            (("1"
                                                                                                                              (lemma
                                                                                                                               "minimum_derivative[posreal]")
                                                                                                                              (("1"
                                                                                                                                (inst
                                                                                                                                 -
                                                                                                                                 "F"
                                                                                                                                 "1"
                                                                                                                                 "z")
                                                                                                                                (("1"
                                                                                                                                  (lemma
                                                                                                                                   "minimum_derivative[posreal]")
                                                                                                                                  (("1"
                                                                                                                                    (inst
                                                                                                                                     -
                                                                                                                                     "G"
                                                                                                                                     "1"
                                                                                                                                     "z")
                                                                                                                                    (("1"
                                                                                                                                      (replace
                                                                                                                                       -3)
                                                                                                                                      (("1"
                                                                                                                                        (replace
                                                                                                                                         -4)
                                                                                                                                        (("1"
                                                                                                                                          (simplify
                                                                                                                                           -1)
                                                                                                                                          (("1"
                                                                                                                                            (simplify
                                                                                                                                             -2)
                                                                                                                                            (("1"
                                                                                                                                              (replace
                                                                                                                                               -9
                                                                                                                                               -1
                                                                                                                                               rl)
                                                                                                                                              (("1"
                                                                                                                                                (replace
                                                                                                                                                 -10
                                                                                                                                                 -2
                                                                                                                                                 rl)
                                                                                                                                                (("1"
                                                                                                                                                  (simplify
                                                                                                                                                   -1)
                                                                                                                                                  (("1"
                                                                                                                                                    (simplify
                                                                                                                                                     -2)
                                                                                                                                                    (("1"
                                                                                                                                                      (rewrite
                                                                                                                                                       "ln_1")
                                                                                                                                                      (("1"
                                                                                                                                                        (simplify
                                                                                                                                                         -2)
                                                                                                                                                        (("1"
                                                                                                                                                          (split
                                                                                                                                                           -1)
                                                                                                                                                          (("1"
                                                                                                                                                            (split
                                                                                                                                                             -2)
                                                                                                                                                            (("1"
                                                                                                                                                              (assert)
                                                                                                                                                              nil
                                                                                                                                                              nil)
                                                                                                                                                             ("2"
                                                                                                                                                              (hide-all-but
                                                                                                                                                               1)
                                                                                                                                                              (("2"
                                                                                                                                                                (skosimp)
                                                                                                                                                                (("2"
                                                                                                                                                                  (rewrite
                                                                                                                                                                   "div_cancel1")
                                                                                                                                                                  (("2"
                                                                                                                                                                    (lemma
                                                                                                                                                                     "trich_lt"
                                                                                                                                                                     ("x"
                                                                                                                                                                      "y!1"
                                                                                                                                                                      "y"
                                                                                                                                                                      "1"))
                                                                                                                                                                    (("2"
                                                                                                                                                                      (split
                                                                                                                                                                       -1)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (lemma
                                                                                                                                                                         "negreal_times_negreal_is_posreal"
                                                                                                                                                                         ("nx"
                                                                                                                                                                          "y!1-1"
                                                                                                                                                                          "ny"
                                                                                                                                                                          "y!1-1"))
                                                                                                                                                                        (("1"
                                                                                                                                                                          (lemma
                                                                                                                                                                           "both_sides_div_pos_gt1"
                                                                                                                                                                           ("x"
                                                                                                                                                                            "(y!1-1)*(y!1-1)"
                                                                                                                                                                            "y"
                                                                                                                                                                            "0"
                                                                                                                                                                            "pz"
                                                                                                                                                                            "y!1"))
                                                                                                                                                                          (("1"
                                                                                                                                                                            (assert)
                                                                                                                                                                            nil
                                                                                                                                                                            nil))
                                                                                                                                                                          nil)
                                                                                                                                                                         ("2"
                                                                                                                                                                          (assert)
                                                                                                                                                                          nil
                                                                                                                                                                          nil))
                                                                                                                                                                        nil)
                                                                                                                                                                       ("2"
                                                                                                                                                                        (propax)
                                                                                                                                                                        nil
                                                                                                                                                                        nil)
                                                                                                                                                                       ("3"
                                                                                                                                                                        (lemma
                                                                                                                                                                         "posreal_times_posreal_is_posreal"
                                                                                                                                                                         ("px"
                                                                                                                                                                          "y!1-1"
                                                                                                                                                                          "py"
                                                                                                                                                                          "y!1-1"))
                                                                                                                                                                        (("1"
                                                                                                                                                                          (lemma
                                                                                                                                                                           "both_sides_div_pos_gt1"
                                                                                                                                                                           ("x"
                                                                                                                                                                            "(y!1-1)*(y!1-1)"
                                                                                                                                                                            "y"
                                                                                                                                                                            "0"
                                                                                                                                                                            "pz"
                                                                                                                                                                            "y!1"))
                                                                                                                                                                          (("1"
                                                                                                                                                                            (assert)
                                                                                                                                                                            nil
                                                                                                                                                                            nil))
                                                                                                                                                                          nil)
                                                                                                                                                                         ("2"
                                                                                                                                                                          (assert)
                                                                                                                                                                          nil
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil)
                                                                                                                                                           ("2"
                                                                                                                                                            (hide-all-but
                                                                                                                                                             1)
                                                                                                                                                            (("2"
                                                                                                                                                              (skosimp*)
                                                                                                                                                              (("2"
                                                                                                                                                                (rewrite
                                                                                                                                                                 "div_cancel1")
                                                                                                                                                                (("2"
                                                                                                                                                                  (lemma
                                                                                                                                                                   "div_times"
                                                                                                                                                                   ("x"
                                                                                                                                                                    "y!1"
                                                                                                                                                                    "n0x"
                                                                                                                                                                    "1"
                                                                                                                                                                    "y"
                                                                                                                                                                    "1"
                                                                                                                                                                    "n0y"
                                                                                                                                                                    "y!1*y!1"))
                                                                                                                                                                  (("2"
                                                                                                                                                                    (replace
                                                                                                                                                                     -1
                                                                                                                                                                     2)
                                                                                                                                                                    (("2"
                                                                                                                                                                      (simplify
                                                                                                                                                                       2)
                                                                                                                                                                      (("2"
                                                                                                                                                                        (simplify
                                                                                                                                                                         2)
                                                                                                                                                                        (("2"
                                                                                                                                                                          (lemma
                                                                                                                                                                           "div_cancel1"
                                                                                                                                                                           ("x"
                                                                                                                                                                            "1/y!1"
                                                                                                                                                                            "n0z"
                                                                                                                                                                            "y!1"))
                                                                                                                                                                          (("2"
                                                                                                                                                                            (rewrite
                                                                                                                                                                             "div_div2"
                                                                                                                                                                             -1)
                                                                                                                                                                            (("2"
                                                                                                                                                                              (replace
                                                                                                                                                                               -1)
                                                                                                                                                                              (("2"
                                                                                                                                                                                (hide
                                                                                                                                                                                 -1)
                                                                                                                                                                                (("2"
                                                                                                                                                                                  (lemma
                                                                                                                                                                                   "trich_lt"
                                                                                                                                                                                   ("x"
                                                                                                                                                                                    "y!1"
                                                                                                                                                                                    "y"
                                                                                                                                                                                    "1"))
                                                                                                                                                                                  (("2"
                                                                                                                                                                                    (split
                                                                                                                                                                                     -1)
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (lemma
                                                                                                                                                                                       "negreal_times_negreal_is_posreal"
                                                                                                                                                                                       ("nx"
                                                                                                                                                                                        "y!1-1"
                                                                                                                                                                                        "ny"
                                                                                                                                                                                        "y!1-1"))
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (lemma
                                                                                                                                                                                         "both_sides_div_pos_gt1"
                                                                                                                                                                                         ("pz"
                                                                                                                                                                                          "y!1*y!1"
                                                                                                                                                                                          "x"
                                                                                                                                                                                          "(y!1-1)*(y!1-1)"
                                                                                                                                                                                          "y"
                                                                                                                                                                                          "0"))
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (assert)
                                                                                                                                                                                          nil
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil)
                                                                                                                                                                                       ("2"
                                                                                                                                                                                        (assert)
                                                                                                                                                                                        nil
                                                                                                                                                                                        nil))
                                                                                                                                                                                      nil)
                                                                                                                                                                                     ("2"
                                                                                                                                                                                      (propax)
                                                                                                                                                                                      nil
                                                                                                                                                                                      nil)
                                                                                                                                                                                     ("3"
                                                                                                                                                                                      (lemma
                                                                                                                                                                                       "posreal_times_posreal_is_posreal"
                                                                                                                                                                                       ("px"
                                                                                                                                                                                        "y!1-1"
                                                                                                                                                                                        "py"
                                                                                                                                                                                        "y!1-1"))
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (lemma
                                                                                                                                                                                         "both_sides_div_pos_gt1"
                                                                                                                                                                                         ("pz"
                                                                                                                                                                                          "y!1*y!1"
                                                                                                                                                                                          "x"
                                                                                                                                                                                          "(y!1-1)*(y!1-1)"
                                                                                                                                                                                          "y"
                                                                                                                                                                                          "0"))
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (assert)
                                                                                                                                                                                          nil
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil)
                                                                                                                                                                                       ("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))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil)
                                                                                           ("2"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil)
                                                                                           ("3"
                                                                                            (propax)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil)
                                                 ("2" (propax) nil nil)
                                                 ("3"
                                                  (propax)
                                                  nil
                                                  nil))
                                                nil))
                                              nil))
                                            nil)
                                           ("2"
                                            (skosimp*)
                                            (("2"
                                              (inst + "x!1+1")
                                              (("2" (assertnil nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (skosimp*)
                                          (("2" (assertnil nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((const_fun const-decl "[T -> real]" real_fun_ops "reals/")
    (ln_1 formula-decl nil ln_exp nil)
    (ln const-decl "real" ln_exp nil))
   shostak))
 (ln_ineq2_TCC1 0
  (ln_ineq2_TCC1-1 nil 3254162049 ("" (grind) nil nilnil shostak))
 (ln_ineq2_TCC2 0
  (ln_ineq2_TCC2-1 nil 3254162049
   ("" (skosimp*) (("" (assertnil nil)) nil)
   ((real_minus_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   shostak))
 (ln_ineq2 0
  (ln_ineq2-1 nil 3254162404
   ("" (skosimp*)
    (("" (typepred "xlt1!1")
      (("" (lemma "ln_ineq1" ("xgtm1" "-xlt1!1"))
        (("" (flatten)
          (("" (lemma "both_sides_times_neg_lt1" ("nz" "-1"))
            (("" (inst-cp - "-xlt1!1" "ln(1 + -xlt1!1)")
              (("" (inst - "ln(1 + -xlt1!1)" "-xlt1!1 / (1 + -xlt1!1)")
                (("" (assertnil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((nzreal_lt1 nonempty-type-eq-decl nil ln_exp_ineq nil)
    (< const-decl "bool" reals nil)
    (nzreal nonempty-type-eq-decl nil reals 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)
    (/= const-decl "boolean" notequal nil)
    (number nonempty-type-decl nil numbers nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (ln const-decl "real" ln_exp nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (minus_real_is_real application-judgement "real" reals nil)
    (nzreal_times_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nzreal_div_nzreal_is_nzreal application-judgement "nzreal"
     real_types nil)
    (negreal nonempty-type-eq-decl nil real_types nil)
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (<= const-decl "bool" reals nil)
    (both_sides_times_neg_lt1 formula-decl nil real_props nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (minus_nzreal_is_nzreal application-judgement "nzreal" real_types
     nil)
    (ln_ineq1 formula-decl nil ln_exp_ineq nil)
    (> const-decl "bool" reals nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (nzreal_gt_m1 nonempty-type-eq-decl nil ln_exp_ineq nil))
   shostak))
 (ln_ineq3_TCC1 0
  (ln_ineq3_TCC1-1 nil 3254162049
   ("" (skosimp*) (("" (assertnil nil)) nil)
   ((real_minus_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak))
 (ln_ineq3 0
  (ln_ineq3-3 nil 3322413185
   ("" (skosimp)
    (("" (expand "abs")
      (("" (lemma "ln_strict_increasing")
        (("" (expand "strict_increasing?")
          (("" (inst - "1-px!1" "1")
            (("1" (rewrite "ln_1")
              (("1" (assert)
                (("1"
                  (lemma "both_sides_plus_lt1"
                   ("z" "ln(1-px!1)" "x" "-ln(1 - px!1)" "y"
                    "3 * px!1 / 2"))
                  (("1" (replace -1 1 rl)
                    (("1" (hide -1)
                      (("1" (simplify 1)
                        (("1" (assert)
                          (("1" (rewrite "inverse_add" 1)
                            (("1" (case "px!1<=1/3")
                              (("1"
                                (lemma "ln_ineq1" ("xgtm1" "-px!1"))
                                (("1"
                                  (flatten)
                                  (("1"
                                    (case "px!1/(1-px!1) <= 3*px!1/2")
                                    (("1" (assertnil nil)
                                     ("2"
                                      (hide -1 -2 -4 -5 2)
                                      (("2"
                                        (lemma
                                         "both_sides_times_pos_le1"
                                         ("pz"
                                          "px!1"
                                          "x"
                                          "1/(1-px!1)"
                                          "y"
                                          "3/2"))
                                        (("2"
                                          (replace -1 1)
                                          (("2"
                                            (hide -1)
                                            (("2"
                                              (rewrite
                                               "div_mult_pos_le1"
                                               1)
                                              (("2"
                                                (lemma
                                                 "both_sides_times_neg_le1"
                                                 ("nz" "-3/2"))
                                                (("2"
                                                  (inst - "1/3" "px!1")
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (case "1/3<px!1")
                                (("1"
                                  (hide 1)
                                  (("1"
                                    (name
                                     "G"
                                     "lambda (x:{x:posreal| 1/3<x&x<1}): ln(1-x) + 3/2*x")
                                    (("1"
                                      (case "G(5828/10000)>0")
                                      (("1"
                                        (case "strict_decreasing?(G)")
                                        (("1"
                                          (expand "strict_decreasing?")
                                          (("1"
                                            (expand "<=" -6)
                                            (("1"
                                              (split -6)
                                              (("1"
                                                (inst
                                                 -
                                                 "px!1"
                                                 "5828/10000")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (expand "G" -2 2)
                                                    (("1"
                                                      (assert)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (replace -1)
                                                (("2"
                                                  (expand "G" -3)
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide -1 2 -4)
                                          (("2"
                                            (lemma
                                             "identity_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]")
                                            (("1"
                                              (lemma
                                               "deriv_id_fun[{x: posreal | 1 / 3 < x & x < 1}]")
                                              (("1"
                                                (lemma
                                                 "const_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                 ("b" "1"))
                                                (("1"
                                                  (lemma
                                                   "deriv_const_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                   ("b" "1"))
                                                  (("1"
                                                    (expand "I")
                                                    (("1"
                                                      (expand
                                                       "const_fun")
                                                      (("1"
                                                        (lemma
                                                         "diff_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                         ("f1"
                                                          "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1"
                                                          "f2"
                                                          "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"))
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (expand
                                                             "-")
                                                            (("1"
                                                              (lemma
                                                               "deriv_diff_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                               ("ff1"
                                                                "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1"
                                                                "ff2"
                                                                "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"))
                                                              (("1"
                                                                (replace
                                                                 -5)
                                                                (("1"
                                                                  (replace
                                                                   -3)
                                                                  (("1"
                                                                    (expand
                                                                     "-")
                                                                    (("1"
                                                                      (lemma
                                                                       "scal_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                       ("f"
                                                                        "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"
                                                                        "b"
                                                                        "3/2"))
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (lemma
                                                                           "deriv_scal_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                           ("ff"
                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"
                                                                            "b"
                                                                            "3/2"))
                                                                          (("1"
                                                                            (replace
                                                                             -7)
                                                                            (("1"
                                                                              (expand
                                                                               "*")
                                                                              (("1"
                                                                                (lemma
                                                                                 "ln_derivable")
                                                                                (("1"
                                                                                  (flatten)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "composition_derivable_fun[{x: posreal | 1 / 3 < x & x < 1},posreal]"
                                                                                     ("f"
                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1 - x"
                                                                                      "g"
                                                                                      "ln"))
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "o")
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "deriv_comp_fun[{x: posreal | 1 / 3 < x & x < 1},posreal]"
                                                                                           ("ff"
                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1 - x"
                                                                                            "gg"
                                                                                            "ln"))
                                                                                          (("1"
                                                                                            (replace
                                                                                             -4)
                                                                                            (("1"
                                                                                              (replace
                                                                                               -7)
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "o")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "*")
                                                                                                  (("1"
                                                                                                    (lemma
                                                                                                     "sum_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                     ("f1"
                                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): ln(1 - x)"
                                                                                                      "f2"
                                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 3 / 2 * x"))
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "+")
                                                                                                        (("1"
                                                                                                          (lemma
                                                                                                           "deriv_sum_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                           ("ff1"
                                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): ln(1 - x)"
                                                                                                            "ff2"
                                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 3 / 2 * x"))
                                                                                                          (("1"
                                                                                                            (replace
                                                                                                             -3)
                                                                                                            (("1"
                                                                                                              (replace
                                                                                                               -7)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "+")
                                                                                                                (("1"
                                                                                                                  (replace
                                                                                                                   -15)
                                                                                                                  (("1"
                                                                                                                    (lemma
                                                                                                                     "negative_derivative[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                                     ("g"
                                                                                                                      "G"))
                                                                                                                    (("1"
                                                                                                                      (split
                                                                                                                       -1)
                                                                                                                      (("1"
                                                                                                                        (propax)
                                                                                                                        nil
                                                                                                                        nil)
                                                                                                                       ("2"
                                                                                                                        (hide
                                                                                                                         2)
                                                                                                                        (("2"
                                                                                                                          (skosimp)
                                                                                                                          (("2"
                                                                                                                            (typepred
                                                                                                                             "x!1")
                                                                                                                            (("2"
                                                                                                                              (expand
                                                                                                                               "deriv"
                                                                                                                               -5)
                                                                                                                              (("2"
                                                                                                                                (lemma
                                                                                                                                 "extensionality_postulate"
                                                                                                                                 ("f"
                                                                                                                                  "(LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): deriv(G, x))"
                                                                                                                                  "g"
                                                                                                                                  "(LAMBDA (x_1: {x: posreal | 1 / 3 < x & x < 1}):
                               3 / 2 + (1 / (1 - x_1)) * -1)"))
                                                                                                                                (("1"
                                                                                                                                  (replace
                                                                                                                                   -1
                                                                                                                                   -6
                                                                                                                                   rl)
                                                                                                                                  (("1"
                                                                                                                                    (hide
                                                                                                                                     -1)
                                                                                                                                    (("1"
                                                                                                                                      (inst
                                                                                                                                       -5
                                                                                                                                       "x!1")
                                                                                                                                      (("1"
                                                                                                                                        (replace
                                                                                                                                         -5)
                                                                                                                                        (("1"
                                                                                                                                          (hide-all-but
                                                                                                                                           (-1
                                                                                                                                            -2
                                                                                                                                            -3
                                                                                                                                            -4
                                                                                                                                            1))
                                                                                                                                          (("1"
                                                                                                                                            (lemma
                                                                                                                                             "div_mult_pos_lt2"
                                                                                                                                             ("z"
                                                                                                                                              "1"
                                                                                                                                              "x"
                                                                                                                                              "3/2"
                                                                                                                                              "py"
                                                                                                                                              "1-x!1"))
                                                                                                                                            (("1"
                                                                                                                                              (assert)
                                                                                                                                              nil
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil)
                                                                                                                                 ("2"
                                                                                                                                  (skosimp*)
                                                                                                                                  (("2"
                                                                                                                                    (typepred
                                                                                                                                     "x!3")
                                                                                                                                    (("2"
                                                                                                                                      (case-replace
                                                                                                                                       "x!3=1/2")
                                                                                                                                      (("1"
                                                                                                                                        (inst
                                                                                                                                         +
                                                                                                                                         "2/3")
                                                                                                                                        (("1"
                                                                                                                                          (assert)
                                                                                                                                          nil
                                                                                                                                          nil))
                                                                                                                                        nil)
                                                                                                                                       ("2"
                                                                                                                                        (inst
                                                                                                                                         +
                                                                                                                                         "1/2")
                                                                                                                                        (("2"
                                                                                                                                          (assert)
                                                                                                                                          nil
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil)
                                                                                                                                 ("3"
                                                                                                                                  (skosimp*)
                                                                                                                                  (("3"
                                                                                                                                    (assert)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil)
                                                                                                                                 ("4"
                                                                                                                                  (expand
                                                                                                                                   "derivable"
                                                                                                                                   -6)
                                                                                                                                  (("4"
                                                                                                                                    (propax)
                                                                                                                                    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"
                                                                                        (inst
                                                                                         +
                                                                                         "2*x!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("3"
                                                                                      (skosimp)
                                                                                      (("3"
                                                                                        (assert)
                                                                                        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"
                                                (case-replace
                                                 "x!1=1/2")
                                                (("1"
                                                  (inst + "2/3")
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (inst + "1/2")
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("3"
                                              (skosimp)
                                              (("3" (assertnil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (hide 2 -3 -2 -4)
                                        (("2"
                                          (replace -1 1 rl)
                                          (("2"
                                            (assert)
                                            (("2"
                                              (hide -1)
                                              (("2"
                                                (lemma
                                                 "ln_estimate_bnd")
                                                (("2"
                                                  (inst
                                                   -
                                                   "19"
                                                   "-5828/10000")
                                                  (("2"
                                                    (assert)
                                                    (("2"
                                                      (expand
                                                       "abs"
                                                       -1
                                                       2)
                                                      (("2"
                                                        (name-replace
                                                         "DRL1"
                                                         "ln(1-5828/10000)")
                                                        (("2"
                                                          (lemma
                                                           "expt_times"
                                                           ("n0x"
                                                            "5828/10000"
                                                            "i"
                                                            "4"
                                                            "j"
                                                            "5"))
                                                          (("2"
                                                            (replace
                                                             -1)
                                                            (("2"
                                                              (case
                                                               "(5828 / 10000) ^ 4 = 1153660896461056 / 10000000000000000")
                                                              (("1"
                                                                (replace
                                                                 -1)
                                                                (("1"
                                                                  (hide
                                                                   -2)
                                                                  (("1"
                                                                    (case-replace
                                                                     "(1153660896461056 / 10000000000000000) ^ 5 /
                    (20 + 20 * (-5828 / 10000)) = (1153660896461056 / 10000000000000000) ^ 5 *10000/83440")
                                                                    (("1"
                                                                      (hide
                                                                       -1)
                                                                      (("1"
                                                                        (case-replace
                                                                         "(1153660896461056 / 10000000000000000) ^ 5 = 2043576321503877532268812309827579231198161568314157086599156544970504011776/100000000000000000000000000000000000000000000000000000000000000000000000000000000")
                                                                        (("1"
                                                                          (hide
                                                                           -1)
                                                                          (("1"
                                                                            (hide
                                                                             -1)
                                                                            (("1"
                                                                              (name
                                                                               "DRL2"
                                                                               "ln_estimate(-5828 / 10000, 19)")
                                                                              (("1"
                                                                                (replace
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                        /
                        100000000000000000000000000000000000000000000000000000000000000000000000000000000
                        * 10000
                        / 83440 = 2043576321503877532268812309827579231198161568314157086599156544970504011776
                        /834400000000000000000000000000000000000000000000000000000000000000000000000000000")
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                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide-all-but
                                                                 1)
                                                                (("2"
                                                                  (grind)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (assertnil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((ln_strict_increasing formula-decl nil ln_exp nil)
    (ln_estimate_bnd formula-decl nil ln_exp_series_alt nil)
    (sigma def-decl "real" sigma "reals/")
    (ln_estimate const-decl "real" ln_exp_series_alt nil)
    (real_gtm1_le1 nonempty-type-eq-decl nil ln_exp_series_alt nil)
    (strict_decreasing? const-decl "bool" real_fun_preds "reals/")
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (const_fun const-decl "[T -> real]" real_fun_ops "reals/")
    (ln const-decl "real" ln_exp nil)
    (ln_1 formula-decl nil ln_exp nil)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/"))
   nil)
  (ln_ineq3-2 nil 3322412713
   ("" (skosimp)
    (("" (expand "abs")
      (("" (lemma "ln_strict_increasing")
        (("" (expand "strict_increasing?")
          (("" (inst - "1-px!1" "1")
            (("1" (rewrite "ln_1")
              (("1" (assert)
                (("1"
                  (lemma "both_sides_plus_lt1"
                   ("z" "ln(1-px!1)" "x" "-ln(1 - px!1)" "y"
                    "3 * px!1 / 2"))
                  (("1" (replace -1 1 rl)
                    (("1" (hide -1)
                      (("1" (simplify 1)
                        (("1" (assert)
                          (("1" (rewrite "inverse_add" 1)
                            (("1" (case "px!1<=1/3")
                              (("1"
                                (lemma "ln_ineq1" ("xgtm1" "-px!1"))
                                (("1"
                                  (flatten)
                                  (("1"
                                    (case "px!1/(1-px!1) <= 3*px!1/2")
                                    (("1" (assertnil)
                                     ("2"
                                      (hide -1 -2 -4 -5 2)
                                      (("2"
                                        (lemma
                                         "both_sides_times_pos_le1"
                                         ("pz"
                                          "px!1"
                                          "x"
                                          "1/(1-px!1)"
                                          "y"
                                          "3/2"))
                                        (("2"
                                          (replace -1 1)
                                          (("2"
                                            (hide -1)
                                            (("2"
                                              (rewrite
                                               "div_mult_pos_le1"
                                               1)
                                              (("2"
                                                (lemma
                                                 "both_sides_times_neg_le1"
                                                 ("nz" "-3/2"))
                                                (("2"
                                                  (inst - "1/3" "px!1")
                                                  (("2"
                                                    (assert)
                                                    nil)))))))))))))))))))))
                               ("2"
                                (case "1/3<px!1")
                                (("1"
                                  (hide 1)
                                  (("1"
                                    (name
                                     "G"
                                     "lambda (x:{x:posreal| 1/3<x&x<1}): ln(1-x) + 3/2*x")
                                    (("1"
                                      (case "G(5828/10000)>0")
                                      (("1"
                                        (case "strict_decreasing?(G)")
                                        (("1"
                                          (expand "strict_decreasing?")
                                          (("1"
                                            (expand "<=" -6)
                                            (("1"
                                              (split -6)
                                              (("1"
                                                (inst
                                                 -
                                                 "px!1"
                                                 "5828/10000")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (expand "G" -2 2)
                                                    (("1"
                                                      (assert)
                                                      nil)))))))
                                               ("2"
                                                (replace -1)
                                                (("2"
                                                  (expand "G" -3)
                                                  (("2"
                                                    (assert)
                                                    nil)))))))))))
                                         ("2"
                                          (hide -1 2 -4)
                                          (("2"
                                            (lemma
                                             "identity_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]")
                                            (("1"
                                              (lemma
                                               "deriv_id_fun[{x: posreal | 1 / 3 < x & x < 1}]")
                                              (("1"
                                                (lemma
                                                 "const_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                 ("b" "1"))
                                                (("1"
                                                  (lemma
                                                   "deriv_const_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                   ("b" "1"))
                                                  (("1"
                                                    (expand "I")
                                                    (("1"
                                                      (expand
                                                       "const_fun")
                                                      (("1"
                                                        (lemma
                                                         "diff_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                         ("f1"
                                                          "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1"
                                                          "f2"
                                                          "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"))
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (expand
                                                             "-")
                                                            (("1"
                                                              (lemma
                                                               "deriv_diff_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                               ("ff1"
                                                                "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1"
                                                                "ff2"
                                                                "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"))
                                                              (("1"
                                                                (replace
                                                                 -5)
                                                                (("1"
                                                                  (replace
                                                                   -3)
                                                                  (("1"
                                                                    (expand
                                                                     "-")
                                                                    (("1"
                                                                      (lemma
                                                                       "scal_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                       ("f"
                                                                        "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"
                                                                        "b"
                                                                        "3/2"))
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (lemma
                                                                           "deriv_scal_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                           ("ff"
                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"
                                                                            "b"
                                                                            "3/2"))
                                                                          (("1"
                                                                            (replace
                                                                             -7)
                                                                            (("1"
                                                                              (expand
                                                                               "*")
                                                                              (("1"
                                                                                (lemma
                                                                                 "ln_derivable")
                                                                                (("1"
                                                                                  (flatten)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "composition_derivable_fun[{x: posreal | 1 / 3 < x & x < 1},posreal]"
                                                                                     ("f"
                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1 - x"
                                                                                      "g"
                                                                                      "ln"))
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "o")
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "deriv_comp_fun[{x: posreal | 1 / 3 < x & x < 1},posreal]"
                                                                                           ("ff"
                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1 - x"
                                                                                            "gg"
                                                                                            "ln"))
                                                                                          (("1"
                                                                                            (replace
                                                                                             -4)
                                                                                            (("1"
                                                                                              (replace
                                                                                               -7)
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "o")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "*")
                                                                                                  (("1"
                                                                                                    (lemma
                                                                                                     "sum_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                     ("f1"
                                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): ln(1 - x)"
                                                                                                      "f2"
                                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 3 / 2 * x"))
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "+")
                                                                                                        (("1"
                                                                                                          (lemma
                                                                                                           "deriv_sum_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                           ("ff1"
                                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): ln(1 - x)"
                                                                                                            "ff2"
                                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 3 / 2 * x"))
                                                                                                          (("1"
                                                                                                            (replace
                                                                                                             -3)
                                                                                                            (("1"
                                                                                                              (replace
                                                                                                               -7)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "+")
                                                                                                                (("1"
                                                                                                                  (replace
                                                                                                                   -15)
                                                                                                                  (("1"
                                                                                                                    (lemma
                                                                                                                     "negative_derivative[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                                     ("g"
                                                                                                                      "G"))
                                                                                                                    (("1"
                                                                                                                      (split
                                                                                                                       -1)
                                                                                                                      (("1"
                                                                                                                        (propax)
                                                                                                                        nil)
                                                                                                                       ("2"
                                                                                                                        (hide
                                                                                                                         2)
                                                                                                                        (("2"
                                                                                                                          (skosimp)
                                                                                                                          (("2"
                                                                                                                            (typepred
                                                                                                                             "x!1")
                                                                                                                            (("2"
                                                                                                                              (expand
                                                                                                                               "deriv"
                                                                                                                               -5)
                                                                                                                              (("2"
                                                                                                                                (lemma
                                                                                                                                 "extensionality_postulate"
                                                                                                                                 ("f"
                                                                                                                                  "(LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): deriv(G, x))"
                                                                                                                                  "g"
                                                                                                                                  "(LAMBDA (x_1: {x: posreal | 1 / 3 < x & x < 1}):
                               3 / 2 + (1 / (1 - x_1)) * -1)"))
                                                                                                                                (("1"
                                                                                                                                  (replace
                                                                                                                                   -1
                                                                                                                                   -6
                                                                                                                                   rl)
                                                                                                                                  (("1"
                                                                                                                                    (hide
                                                                                                                                     -1)
                                                                                                                                    (("1"
                                                                                                                                      (inst
                                                                                                                                       -5
                                                                                                                                       "x!1")
                                                                                                                                      (("1"
                                                                                                                                        (replace
                                                                                                                                         -5)
                                                                                                                                        (("1"
                                                                                                                                          (hide-all-but
                                                                                                                                           (-1
                                                                                                                                            -2
                                                                                                                                            -3
                                                                                                                                            -4
                                                                                                                                            1))
                                                                                                                                          (("1"
                                                                                                                                            (lemma
                                                                                                                                             "div_mult_pos_lt2"
                                                                                                                                             ("z"
                                                                                                                                              "1"
                                                                                                                                              "x"
                                                                                                                                              "3/2"
                                                                                                                                              "py"
                                                                                                                                              "1-x!1"))
                                                                                                                                            (("1"
                                                                                                                                              (assert)
                                                                                                                                              nil)))))))))))))
                                                                                                                                 ("2"
                                                                                                                                  (skosimp*)
                                                                                                                                  (("2"
                                                                                                                                    (typepred
                                                                                                                                     "x!3")
                                                                                                                                    (("2"
                                                                                                                                      (case-replace
                                                                                                                                       "x!3=1/2")
                                                                                                                                      (("1"
                                                                                                                                        (inst
                                                                                                                                         +
                                                                                                                                         "2/3")
                                                                                                                                        (("1"
                                                                                                                                          (assert)
                                                                                                                                          nil)))
                                                                                                                                       ("2"
                                                                                                                                        (inst
                                                                                                                                         +
                                                                                                                                         "1/2")
                                                                                                                                        (("2"
                                                                                                                                          (assert)
                                                                                                                                          nil)))))))))
                                                                                                                                 ("3"
                                                                                                                                  (skosimp*)
                                                                                                                                  (("3"
                                                                                                                                    (assert)
                                                                                                                                    nil)))
                                                                                                                                 ("4"
                                                                                                                                  (expand
                                                                                                                                   "derivable"
                                                                                                                                   -6)
                                                                                                                                  (("4"
                                                                                                                                    (propax)
                                                                                                                                    nil)))))))))))))))
                                                                                                                     ("2"
                                                                                                                      (propax)
                                                                                                                      nil)))))))))))))))))))))))))))))))))
                                                                                     ("2"
                                                                                      (skosimp)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "2*x!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil)))))
                                                                                     ("3"
                                                                                      (skosimp)
                                                                                      (("3"
                                                                                        (assert)
                                                                                        nil)))))))))))))))))))))))))))))))))))))))))))
                                             ("2"
                                              (skosimp)
                                              (("2"
                                                (case-replace
                                                 "x!1=1/2")
                                                (("1"
                                                  (inst + "2/3")
                                                  (("1" (assertnil)))
                                                 ("2"
                                                  (inst + "1/2")
                                                  (("2"
                                                    (assert)
                                                    nil)))))))
                                             ("3"
                                              (skosimp)
                                              (("3"
                                                (assert)
                                                nil)))))))))
                                       ("2"
                                        (hide 2 -3 -2 -4)
                                        (("2"
                                          (replace -1 1 rl)
                                          (("2"
                                            (assert)
                                            (("2"
                                              (hide -1)
                                              (("2"
                                                (lemma "ln_estimate")
                                                (("2"
                                                  (inst
                                                   -
                                                   "19"
                                                   "-5828/10000")
                                                  (("2"
                                                    (assert)
                                                    (("2"
                                                      (expand
                                                       "abs"
                                                       -1
                                                       2)
                                                      (("2"
                                                        (name-replace
                                                         "DRL1"
                                                         "ln(1-5828/10000)")
                                                        (("2"
                                                          (lemma
                                                           "expt_times"
                                                           ("n0x"
                                                            "5828/10000"
                                                            "i"
                                                            "4"
                                                            "j"
                                                            "5"))
                                                          (("2"
                                                            (replace
                                                             -1)
                                                            (("2"
                                                              (case
                                                               "(5828 / 10000) ^ 4 = 1153660896461056 / 10000000000000000")
                                                              (("1"
                                                                (replace
                                                                 -1)
                                                                (("1"
                                                                  (hide
                                                                   -2)
                                                                  (("1"
                                                                    (case-replace
                                                                     "(1153660896461056 / 10000000000000000) ^ 5 /
                    (20 + 20 * (-5828 / 10000)) = (1153660896461056 / 10000000000000000) ^ 5 *10000/83440")
                                                                    (("1"
                                                                      (hide
                                                                       -1)
                                                                      (("1"
                                                                        (case-replace
                                                                         "(1153660896461056 / 10000000000000000) ^ 5 = 2043576321503877532268812309827579231198161568314157086599156544970504011776/100000000000000000000000000000000000000000000000000000000000000000000000000000000")
                                                                        (("1"
                                                                          (hide
                                                                           -1)
                                                                          (("1"
                                                                            (hide
                                                                             -1)
                                                                            (("1"
                                                                              (name
                                                                               "DRL2"
                                                                               "ln_estimate(-5828 / 10000, 19)")
                                                                              (("1"
                                                                                (replace
                                                                                 -1)
                                                                                (("1"
                                                                                  (case-replace
                                                                                   "2043576321503877532268812309827579231198161568314157086599156544970504011776
                        /
                        100000000000000000000000000000000000000000000000000000000000000000000000000000000
                        * 10000
                        / 83440 = 2043576321503877532268812309827579231198161568314157086599156544970504011776
                        /834400000000000000000000000000000000000000000000000000000000000000000000000000000")
                                                                                  (("1"
                                                                                    (hide
                                                                                     -1)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "ln_estimate")
                                                                                      (("1"
                                                                                        (expand
                                                                                         "sigma")
                                                                                        (("1"
                                                                                          (expand
                                                                                           "sigma")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "sigma")
                                                                                            (("1"
                                                                                              (expand
                                                                                               "sigma")
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "sigma")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "sigma")
                                                                                                  (("1"
                                                                                                    (expand
                                                                                                     "sigma")
                                                                                                    (("1"
                                                                                                      (expand
                                                                                                       "sigma")
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "sigma")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "sigma")
                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "sigma")
                                                                                                            (("1"
                                                                                                              (expand
                                                                                                               "sigma")
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "sigma")
                                                                                                                (("1"
                                                                                                                  (expand
                                                                                                                   "sigma")
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     "sigma")
                                                                                                                    (("1"
                                                                                                                      (expand
                                                                                                                       "sigma")
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "sigma")
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "sigma")
                                                                                                                          (("1"
                                                                                                                            (expand
                                                                                                                             "sigma")
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "sigma")
                                                                                                                              (("1"
                                                                                                                                (case-replace
                                                                                                                                 "-(-5828 / 10000) = 5828/10000")
                                                                                                                                (("1"
                                                                                                                                  (hide
                                                                                                                                   -1)
                                                                                                                                  (("1"
                                                                                                                                    (lemma
                                                                                                                                     "expt_times"
                                                                                                                                     ("n0x"
                                                                                                                                      "5828/10000"))
                                                                                                                                    (("1"
                                                                                                                                      (lemma
                                                                                                                                       "expt_plus"
                                                                                                                                       ("n0x"
                                                                                                                                        "5828/10000"))
                                                                                                                                      (("1"
                                                                                                                                        (rewrite
                                                                                                                                         "expt_x1"
                                                                                                                                         -3)
                                                                                                                                        (("1"
                                                                                                                                          (case
                                                                                                                                           "(5828 / 10000) ^ 2 = 33965584/100000000")
                                                                                                                                          (("1"
                                                                                                                                            (replace
                                                                                                                                             -1)
                                                                                                                                            (("1"
                                                                                                                                              (inst-cp
                                                                                                                                               -
                                                                                                                                               "1"
                                                                                                                                               "2")
                                                                                                                                              (("1"
                                                                                                                                                (lemma
                                                                                                                                                 "expt_x1")
                                                                                                                                                (("1"
                                                                                                                                                  (inst
                                                                                                                                                   -
                                                                                                                                                   "5828/10000")
                                                                                                                                                  (("1"
                                                                                                                                                    (replace
                                                                                                                                                     -1)
                                                                                                                                                    (("1"
                                                                                                                                                      (replace
                                                                                                                                                       -2)
                                                                                                                                                      (("1"
                                                                                                                                                        (replace
                                                                                                                                                         -4)
                                                                                                                                                        (("1"
                                                                                                                                                          (case-replace
                                                                                                                                                           "5828 / 10000 * (33965584 / 100000000) = 197951423552/1000000000000")
                                                                                                                                                          (("1"
                                                                                                                                                            (hide
                                                                                                                                                             -1)
                                                                                                                                                            (("1"
                                                                                                                                                              (inst-cp
                                                                                                                                                               -
                                                                                                                                                               "2"
                                                                                                                                                               "2")
                                                                                                                                                              (("1"
                                                                                                                                                                (replace
                                                                                                                                                                 -2)
                                                                                                                                                                (("1"
                                                                                                                                                                  (case-replace
                                                                                                                                                                   "33965584 / 100000000 * (33965584 / 100000000) = 1153660896461056 / 10000000000000000")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (hide
                                                                                                                                                                     -1)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (replace
                                                                                                                                                                       -4)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (inst-cp
                                                                                                                                                                         -
                                                                                                                                                                         "2"
                                                                                                                                                                         "3")
                                                                                                                                                                        (("1"
                                                                                                                                                                          (replace
                                                                                                                                                                           -2)
                                                                                                                                                                          (("1"
                                                                                                                                                                            (replace
                                                                                                                                                                             -6)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (case-replace
                                                                                                                                                                               "33965584 / 100000000 * (197951423552 / 1000000000000) = 6723535704575034368/100000000000000000000")
                                                                                                                                                                              (("1"
                                                                                                                                                                                (replace
                                                                                                                                                                                 -5)
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (hide
                                                                                                                                                                                   -1)
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (inst-cp
                                                                                                                                                                                     -
                                                                                                                                                                                     "3"
                                                                                                                                                                                     "3")
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (replace
                                                                                                                                                                                       -7)
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (case-replace
                                                                                                                                                                                         "197951423552 / 1000000000000 * (197951423552 / 1000000000000) = 39184766086263300296704/1000000000000000000000000")
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (hide
                                                                                                                                                                                           -1)
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (replace
                                                                                                                                                                                             -4)
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (simplify
                                                                                                                                                                                               -4)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (simplify
                                                                                                                                                                                                 -5)
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (simplify
                                                                                                                                                                                                   -6)
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (simplify
                                                                                                                                                                                                     -7)
                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                      (inst-cp
                                                                                                                                                                                                       -
                                                                                                                                                                                                       "3"
                                                                                                                                                                                                       "4")
                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                        (replace
                                                                                                                                                                                                         -8)
                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                          (replace
                                                                                                                                                                                                           -7)
                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                            (simplify
                                                                                                                                                                                                             -4)
                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                              (replace
                                                                                                                                                                                                               -4)
                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                (hide
                                                                                                                                                                                                                 -9)
                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                  (inst-cp
                                                                                                                                                                                                                   -
                                                                                                                                                                                                                   "4"
                                                                                                                                                                                                                   "4")
                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                     -8)
                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                       -4)
                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                        (inst-cp
                                                                                                                                                                                                                         -
                                                                                                                                                                                                                         "4"
                                                                                                                                                                                                                         "5")
                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                           -8)
                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                             -9)
                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                              (replace
                                                                                                                                                                                                                               -4)
                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                (inst-cp
                                                                                                                                                                                                                                 -
                                                                                                                                                                                                                                 "5"
                                                                                                                                                                                                                                 "5")
                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                   -9)
                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                                     -4)
                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                      (inst-cp
                                                                                                                                                                                                                                       -
                                                                                                                                                                                                                                       "5"
                                                                                                                                                                                                                                       "6")
                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                         -9)
                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                           -10)
                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                             -4)
                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                              (inst-cp
                                                                                                                                                                                                                                               -
                                                                                                                                                                                                                                               "6"
                                                                                                                                                                                                                                               "6")
                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                                                 -10)
                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                                   -4)
                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                    (case-replace
                                                                                                                                                                                                                                                     "(197951423552 / 1000000000000 *
                                        (1153660896461056 / 10000000000000000)) = 228368816750742514129190912/10000000000000000000000000000")
                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                      (hide
                                                                                                                                                                                                                                                       -1)
                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                        (inst-cp
                                                                                                                                                                                                                                                         -
                                                                                                                                                                                                                                                         "6"
                                                                                                                                                                                                                                                         "7")
                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                                           -10)
                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                                             -11)
                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                              (replace
                                                                                                                                                                                                                                                               -4)
                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                (inst-cp
                                                                                                                                                                                                                                                                 -
                                                                                                                                                                                                                                                                 "7"
                                                                                                                                                                                                                                                                 "7")
                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                                                   -11)
                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                                                                     -4)
                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                      (inst-cp
                                                                                                                                                                                                                                                                       -
                                                                                                                                                                                                                                                                       "7"
                                                                                                                                                                                                                                                                       "8")
                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                                                         -12)
                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                                                           -11)
                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                                                             -4)
                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                              (inst-cp
                                                                                                                                                                                                                                                                               -
                                                                                                                                                                                                                                                                               "8"
                                                                                                                                                                                                                                                                               "8")
                                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                                                                                 -12)
                                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                                                                   -4)
                                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                                    (inst-cp
                                                                                                                                                                                                                                                                                     -
                                                                                                                                                                                                                                                                                     "8"
                                                                                                                                                                                                                                                                                     "9")
                                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                                                                                       -12)
                                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                                                                         -13)
                                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                                                                           -4)
                                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                                            (inst-cp
                                                                                                                                                                                                                                                                                             -
                                                                                                                                                                                                                                                                                             "9"
                                                                                                                                                                                                                                                                                             "9")
                                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                                              (replace
                                                                                                                                                                                                                                                                                               -13)
                                                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                                                                                                 -4)
                                                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                                                  (inst
                                                                                                                                                                                                                                                                                                   -
                                                                                                                                                                                                                                                                                                   "9"
                                                                                                                                                                                                                                                                                                   "10")
                                                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                                                                                                     -12)
                                                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                                                                                                       -13)
                                                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                                                                                         -3)
                                                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                                                          (hide-all-but
                                                                                                                                                                                                                                                                                                           (-20
                                                                                                                                                                                                                                                                                                            -21
                                                                                                                                                                                                                                                                                                            1))
                                                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                                                            (expand
                                                                                                                                                                                                                                                                                                             "abs"
                                                                                                                                                                                                                                                                                                             -2)
                                                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                                                              (assert)
                                                                                                                                                                                                                                                                                                              nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))))
                                                                                                                                                                                                                                                     ("2"
                                                                                                                                                                                                                                                      (assert)
                                                                                                                                                                                                                                                      nil)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
                                                                                                                                                                                         ("2"
                                                                                                                                                                                          (assert)
                                                                                                                                                                                          nil)))))))))))
                                                                                                                                                                               ("2"
                                                                                                                                                                                (assert)
                                                                                                                                                                                nil)))))))))))))
                                                                                                                                                                   ("2"
                                                                                                                                                                    (assert)
                                                                                                                                                                    nil)))))))))
                                                                                                                                                           ("2"
                                                                                                                                                            (assert)
                                                                                                                                                            nil)))))))))))))))))
                                                                                                                                           ("2"
                                                                                                                                            (expand
                                                                                                                                             "^"
                                                                                                                                             1)
                                                                                                                                            (("2"
                                                                                                                                              (expand
                                                                                                                                               "expt")
                                                                                                                                              (("2"
                                                                                                                                                (expand
                                                                                                                                                 "expt")
                                                                                                                                                (("2"
                                                                                                                                                  (expand
                                                                                                                                                   "expt")
                                                                                                                                                  (("2"
                                                                                                                                                    (assert)
                                                                                                                                                    nil)))))))))))))))))))
                                                                                                                                 ("2"
                                                                                                                                  (assert)
                                                                                                                                  nil)))))))))))))))))))))))))))))))))))))))))))))))
                                                                                   ("2"
                                                                                    (assert)
                                                                                    nil)))))))))))
                                                                         ("2"
                                                                          (hide-all-but
                                                                           1)
                                                                          (("2"
                                                                            (expand
                                                                             "^")
                                                                            (("2"
                                                                              (expand
                                                                               "expt")
                                                                              (("2"
                                                                                (expand
                                                                                 "expt")
                                                                                (("2"
                                                                                  (expand
                                                                                   "expt")
                                                                                  (("2"
                                                                                    (expand
                                                                                     "expt")
                                                                                    (("2"
                                                                                      (expand
                                                                                       "expt")
                                                                                      (("2"
                                                                                        (expand
                                                                                         "expt")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil)))))))))))))))))))))
                                                                     ("2"
                                                                      (hide-all-but
                                                                       1)
                                                                      (("2"
                                                                        (assert)
                                                                        nil)))))))))
                                                               ("2"
                                                                (hide-all-but
                                                                 1)
                                                                (("2"
                                                                  (grind)
                                                                  nil)))))))))))))))))))))))))))))))))
                                 ("2" (assertnil)))))))))))))))))))))
             ("2" (assertnil))))))))))
    nil)
   nil nil)
  (ln_ineq3-1 nil 3254163549
   ("" (skosimp)
    (("" (expand "abs")
      (("" (lemma "ln_strict_increasing")
        (("" (expand "strict_increasing?")
          (("" (inst - "1-px!1" "1")
            (("1" (rewrite "ln_1")
              (("1" (assert)
                (("1"
                  (lemma "both_sides_plus_lt1"
                   ("z" "ln(1-px!1)" "x" "-ln(1 - px!1)" "y"
                    "3 * px!1 / 2"))
                  (("1" (replace -1 1 rl)
                    (("1" (hide -1)
                      (("1" (simplify 1)
                        (("1" (assert)
                          (("1" (rewrite "inverse_add" 1)
                            (("1" (case "px!1<=1/3")
                              (("1"
                                (lemma "ln_ineq1" ("xgtm1" "-px!1"))
                                (("1"
                                  (flatten)
                                  (("1"
                                    (case "px!1/(1-px!1) <= 3*px!1/2")
                                    (("1" (assertnil nil)
                                     ("2"
                                      (hide -1 -2 -4 -5 2)
                                      (("2"
                                        (lemma
                                         "both_sides_times_pos_le1"
                                         ("pz"
                                          "px!1"
                                          "x"
                                          "1/(1-px!1)"
                                          "y"
                                          "3/2"))
                                        (("2"
                                          (replace -1 1)
                                          (("2"
                                            (hide -1)
                                            (("2"
                                              (rewrite
                                               "div_mult_pos_le1"
                                               1)
                                              (("2"
                                                (lemma
                                                 "both_sides_times_neg_le1"
                                                 ("nz" "-3/2"))
                                                (("2"
                                                  (inst - "1/3" "px!1")
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (case "1/3<px!1")
                                (("1"
                                  (hide 1)
                                  (("1"
                                    (name
                                     "G"
                                     "lambda (x:{x:posreal| 1/3<x&x<1}): ln(1-x) + 3/2*x")
                                    (("1"
                                      (case "G(5828/10000)>0")
                                      (("1"
                                        (case "strict_decreasing?(G)")
                                        (("1"
                                          (expand "strict_decreasing?")
                                          (("1"
                                            (expand "<=" -6)
                                            (("1"
                                              (split -6)
                                              (("1"
                                                (inst
                                                 -
                                                 "px!1"
                                                 "5828/10000")
                                                (("1"
                                                  (assert)
                                                  (("1"
                                                    (expand "G" -2 2)
                                                    (("1"
                                                      (assert)
                                                      nil
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil)
                                               ("2"
                                                (replace -1)
                                                (("2"
                                                  (expand "G" -3)
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil)
                                         ("2"
                                          (hide -1 2 -4)
                                          (("2"
                                            (lemma
                                             "identity_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]")
                                            (("1"
                                              (lemma
                                               "deriv_id_fun[{x: posreal | 1 / 3 < x & x < 1}]")
                                              (("1"
                                                (lemma
                                                 "const_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                 ("b" "1"))
                                                (("1"
                                                  (lemma
                                                   "deriv_const_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                   ("b" "1"))
                                                  (("1"
                                                    (expand "I")
                                                    (("1"
                                                      (expand
                                                       "const_fun")
                                                      (("1"
                                                        (lemma
                                                         "diff_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                         ("f1"
                                                          "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1"
                                                          "f2"
                                                          "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"))
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (expand
                                                             "-")
                                                            (("1"
                                                              (lemma
                                                               "deriv_diff_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                               ("ff1"
                                                                "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1"
                                                                "ff2"
                                                                "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"))
                                                              (("1"
                                                                (replace
                                                                 -5)
                                                                (("1"
                                                                  (replace
                                                                   -3)
                                                                  (("1"
                                                                    (expand
                                                                     "-")
                                                                    (("1"
                                                                      (lemma
                                                                       "scal_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                       ("f"
                                                                        "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"
                                                                        "b"
                                                                        "3/2"))
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (lemma
                                                                           "deriv_scal_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                           ("ff"
                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): x"
                                                                            "b"
                                                                            "3/2"))
                                                                          (("1"
                                                                            (replace
                                                                             -7)
                                                                            (("1"
                                                                              (expand
                                                                               "*")
                                                                              (("1"
                                                                                (lemma
                                                                                 "ln_derivable")
                                                                                (("1"
                                                                                  (flatten)
                                                                                  (("1"
                                                                                    (lemma
                                                                                     "composition_derivable_fun[{x: posreal | 1 / 3 < x & x < 1},posreal]"
                                                                                     ("f"
                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1 - x"
                                                                                      "g"
                                                                                      "ln"))
                                                                                    (("1"
                                                                                      (assert)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "o")
                                                                                        (("1"
                                                                                          (lemma
                                                                                           "deriv_comp_fun[{x: posreal | 1 / 3 < x & x < 1},posreal]"
                                                                                           ("ff"
                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 1 - x"
                                                                                            "gg"
                                                                                            "ln"))
                                                                                          (("1"
                                                                                            (replace
                                                                                             -4)
                                                                                            (("1"
                                                                                              (replace
                                                                                               -7)
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "o")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "*")
                                                                                                  (("1"
                                                                                                    (lemma
                                                                                                     "sum_derivable_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                     ("f1"
                                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): ln(1 - x)"
                                                                                                      "f2"
                                                                                                      "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 3 / 2 * x"))
                                                                                                    (("1"
                                                                                                      (assert)
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "+")
                                                                                                        (("1"
                                                                                                          (lemma
                                                                                                           "deriv_sum_fun[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                           ("ff1"
                                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): ln(1 - x)"
                                                                                                            "ff2"
                                                                                                            "LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): 3 / 2 * x"))
                                                                                                          (("1"
                                                                                                            (replace
                                                                                                             -3)
                                                                                                            (("1"
                                                                                                              (replace
                                                                                                               -7)
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "+")
                                                                                                                (("1"
                                                                                                                  (replace
                                                                                                                   -15)
                                                                                                                  (("1"
                                                                                                                    (lemma
                                                                                                                     "negative_derivative[{x: posreal | 1 / 3 < x & x < 1}]"
                                                                                                                     ("g"
                                                                                                                      "G"))
                                                                                                                    (("1"
                                                                                                                      (split
                                                                                                                       -1)
                                                                                                                      (("1"
                                                                                                                        (propax)
                                                                                                                        nil
                                                                                                                        nil)
                                                                                                                       ("2"
                                                                                                                        (hide
                                                                                                                         2)
                                                                                                                        (("2"
                                                                                                                          (skosimp)
                                                                                                                          (("2"
                                                                                                                            (typepred
                                                                                                                             "x!1")
                                                                                                                            (("2"
                                                                                                                              (expand
                                                                                                                               "deriv"
                                                                                                                               -5)
                                                                                                                              (("2"
                                                                                                                                (lemma
                                                                                                                                 "extensionality_postulate"
                                                                                                                                 ("f"
                                                                                                                                  "(LAMBDA (x: {x: posreal | 1 / 3 < x & x < 1}): deriv(G, x))"
                                                                                                                                  "g"
                                                                                                                                  "(LAMBDA (x_1: {x: posreal | 1 / 3 < x & x < 1}):
          3 / 2 + (1 / (1 - x_1)) * -1)"))
                                                                                                                                (("1"
                                                                                                                                  (replace
                                                                                                                                   -1
                                                                                                                                   -6
                                                                                                                                   rl)
                                                                                                                                  (("1"
                                                                                                                                    (hide
                                                                                                                                     -1)
                                                                                                                                    (("1"
                                                                                                                                      (inst
                                                                                                                                       -5
                                                                                                                                       "x!1")
                                                                                                                                      (("1"
                                                                                                                                        (replace
                                                                                                                                         -5)
                                                                                                                                        (("1"
                                                                                                                                          (hide-all-but
                                                                                                                                           (-1
                                                                                                                                            -2
                                                                                                                                            -3
                                                                                                                                            -4
                                                                                                                                            1))
                                                                                                                                          (("1"
                                                                                                                                            (lemma
                                                                                                                                             "div_mult_pos_lt2"
                                                                                                                                             ("z"
                                                                                                                                              "1"
                                                                                                                                              "x"
                                                                                                                                              "3/2"
                                                                                                                                              "py"
                                                                                                                                              "1-x!1"))
                                                                                                                                            (("1"
                                                                                                                                              (assert)
                                                                                                                                              nil
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil)
                                                                                                                                 ("2"
                                                                                                                                  (skosimp*)
                                                                                                                                  (("2"
                                                                                                                                    (typepred
                                                                                                                                     "x!3")
                                                                                                                                    (("2"
                                                                                                                                      (case-replace
                                                                                                                                       "x!3=1/2")
                                                                                                                                      (("1"
                                                                                                                                        (inst
                                                                                                                                         +
                                                                                                                                         "2/3")
                                                                                                                                        (("1"
                                                                                                                                          (assert)
                                                                                                                                          nil
                                                                                                                                          nil))
                                                                                                                                        nil)
                                                                                                                                       ("2"
                                                                                                                                        (inst
                                                                                                                                         +
                                                                                                                                         "1/2")
                                                                                                                                        (("2"
                                                                                                                                          (assert)
                                                                                                                                          nil
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil)
                                                                                                                                 ("3"
                                                                                                                                  (skosimp*)
                                                                                                                                  (("3"
                                                                                                                                    (assert)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil)
                                                                                                                                 ("4"
                                                                                                                                  (expand
                                                                                                                                   "derivable"
                                                                                                                                   -6)
                                                                                                                                  (("4"
                                                                                                                                    (propax)
                                                                                                                                    nil
                                                                                                                                    nil))
                                                                                                                                  nil))
                                                                                                                                nil))
                                                                                                                              nil))
                                                                                                                            nil))
                                                                                                                          nil))
                                                                                                                        nil))
                                                                                                                      nil)
                                                                                                                     ("2"
                                                                                                                      (propax)
                                                                                                                      nil
                                                                                                                      nil))
                                                                                                                    nil))
                                                                                                                  nil))
                                                                                                                nil))
                                                                                                              nil))
                                                                                                            nil))
                                                                                                          nil))
                                                                                                        nil))
                                                                                                      nil))
                                                                                                    nil))
                                                                                                  nil))
                                                                                                nil))
                                                                                              nil))
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("2"
                                                                                      (skosimp)
                                                                                      (("2"
                                                                                        (inst
                                                                                         +
                                                                                         "2*x!1")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil)
                                                                                     ("3"
                                                                                      (skosimp)
                                                                                      (("3"
                                                                                        (assert)
                                                                                        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"
                                                (case-replace
                                                 "x!1=1/2")
                                                (("1"
                                                  (inst + "2/3")
                                                  (("1"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil)
                                                 ("2"
                                                  (inst + "1/2")
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil)
                                             ("3"
                                              (skosimp)
                                              (("3" (assertnil nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2"
                                        (hide 2 -3 -2 -4)
                                        (("2"
                                          (replace -1 1 rl)
                                          (("2"
                                            (assert)
                                            (("2"
                                              (hide -1)
                                              (("2"
                                                (lemma "ln_series")
                                                (("2"
                                                  (inst
                                                   -
                                                   "19"
                                                   "-5828/10000")
                                                  (("2"
                                                    (assert)
                                                    (("2"
                                                      (expand
                                                       "abs"
                                                       -1
                                                       2)
                                                      (("2"
                                                        (name-replace
                                                         "DRL1"
                                                         "ln(1-5828/10000)")
                                                        (("2"
                                                          (lemma
                                                           "expt_times"
                                                           ("n0x"
                                                            "5828/10000"
                                                            "i"
                                                            "4"
                                                            "j"
                                                            "5"))
                                                          (("2"
                                                            (replace
                                                             -1)
                                                            (("2"
                                                              (case
                                                               "(5828 / 10000) ^ 4 = 1153660896461056 / 10000000000000000")
                                                              (("1"
                                                                (replace
                                                                 -1)
                                                                (("1"
                                                                  (hide
                                                                   -2)
                                                                  (("1"
                                                                    (case-replace
                                                                     "(1153660896461056 / 10000000000000000) ^ 5 /
        (20 + 20 * (-5828 / 10000)) = (1153660896461056 / 10000000000000000) ^ 5 *10000/83440")
                                                                    (("1"
                                                                      (hide
                                                                       -1)
                                                                      (("1"
                                                                        (case-replace
                                                                         "(1153660896461056 / 10000000000000000) ^ 5 = 2043576321503877532268812309827579231198161568314157086599156544970504011776/100000000000000000000000000000000000000000000000000000000000000000000000000000000")
                                                                        (("1"
                                                                          (hide
                                                                           -1)
                                                                          (("1"
                                                                            (hide
                                                                             -1)
                                                                            (("1"
                                                                              (name
                                                                               "DRL2"
                                                                               "ln_estimate(-5828 / 10000, 19)")
                                                                              (("1"
                                                                                (replace
                                                                                 -1)
                                                                                (("1"
                                                                                  (case-replace
                                                                                   "2043576321503877532268812309827579231198161568314157086599156544970504011776
        /
        100000000000000000000000000000000000000000000000000000000000000000000000000000000
        * 10000
        / 83440 = 2043576321503877532268812309827579231198161568314157086599156544970504011776
        /834400000000000000000000000000000000000000000000000000000000000000000000000000000")
                                                                                  (("1"
                                                                                    (hide
                                                                                     -1)
                                                                                    (("1"
                                                                                      (expand
                                                                                       "ln_estimate")
                                                                                      (("1"
                                                                                        (expand
                                                                                         "sigma")
                                                                                        (("1"
                                                                                          (expand
                                                                                           "sigma")
                                                                                          (("1"
                                                                                            (expand
                                                                                             "sigma")
                                                                                            (("1"
                                                                                              (expand
                                                                                               "sigma")
                                                                                              (("1"
                                                                                                (expand
                                                                                                 "sigma")
                                                                                                (("1"
                                                                                                  (expand
                                                                                                   "sigma")
                                                                                                  (("1"
                                                                                                    (expand
                                                                                                     "sigma")
                                                                                                    (("1"
                                                                                                      (expand
                                                                                                       "sigma")
                                                                                                      (("1"
                                                                                                        (expand
                                                                                                         "sigma")
                                                                                                        (("1"
                                                                                                          (expand
                                                                                                           "sigma")
                                                                                                          (("1"
                                                                                                            (expand
                                                                                                             "sigma")
                                                                                                            (("1"
                                                                                                              (expand
                                                                                                               "sigma")
                                                                                                              (("1"
                                                                                                                (expand
                                                                                                                 "sigma")
                                                                                                                (("1"
                                                                                                                  (expand
                                                                                                                   "sigma")
                                                                                                                  (("1"
                                                                                                                    (expand
                                                                                                                     "sigma")
                                                                                                                    (("1"
                                                                                                                      (expand
                                                                                                                       "sigma")
                                                                                                                      (("1"
                                                                                                                        (expand
                                                                                                                         "sigma")
                                                                                                                        (("1"
                                                                                                                          (expand
                                                                                                                           "sigma")
                                                                                                                          (("1"
                                                                                                                            (expand
                                                                                                                             "sigma")
                                                                                                                            (("1"
                                                                                                                              (expand
                                                                                                                               "sigma")
                                                                                                                              (("1"
                                                                                                                                (case-replace
                                                                                                                                 "-(-5828 / 10000) = 5828/10000")
                                                                                                                                (("1"
                                                                                                                                  (hide
                                                                                                                                   -1)
                                                                                                                                  (("1"
                                                                                                                                    (lemma
                                                                                                                                     "expt_times"
                                                                                                                                     ("n0x"
                                                                                                                                      "5828/10000"))
                                                                                                                                    (("1"
                                                                                                                                      (lemma
                                                                                                                                       "expt_plus"
                                                                                                                                       ("n0x"
                                                                                                                                        "5828/10000"))
                                                                                                                                      (("1"
                                                                                                                                        (rewrite
                                                                                                                                         "expt_x1"
                                                                                                                                         -3)
                                                                                                                                        (("1"
                                                                                                                                          (case
                                                                                                                                           "(5828 / 10000) ^ 2 = 33965584/100000000")
                                                                                                                                          (("1"
                                                                                                                                            (replace
                                                                                                                                             -1)
                                                                                                                                            (("1"
                                                                                                                                              (inst-cp
                                                                                                                                               -
                                                                                                                                               "1"
                                                                                                                                               "2")
                                                                                                                                              (("1"
                                                                                                                                                (lemma
                                                                                                                                                 "expt_x1")
                                                                                                                                                (("1"
                                                                                                                                                  (inst
                                                                                                                                                   -
                                                                                                                                                   "5828/10000")
                                                                                                                                                  (("1"
                                                                                                                                                    (replace
                                                                                                                                                     -1)
                                                                                                                                                    (("1"
                                                                                                                                                      (replace
                                                                                                                                                       -2)
                                                                                                                                                      (("1"
                                                                                                                                                        (replace
                                                                                                                                                         -4)
                                                                                                                                                        (("1"
                                                                                                                                                          (case-replace
                                                                                                                                                           "5828 / 10000 * (33965584 / 100000000) = 197951423552/1000000000000")
                                                                                                                                                          (("1"
                                                                                                                                                            (hide
                                                                                                                                                             -1)
                                                                                                                                                            (("1"
                                                                                                                                                              (inst-cp
                                                                                                                                                               -
                                                                                                                                                               "2"
                                                                                                                                                               "2")
                                                                                                                                                              (("1"
                                                                                                                                                                (replace
                                                                                                                                                                 -2)
                                                                                                                                                                (("1"
                                                                                                                                                                  (case-replace
                                                                                                                                                                   "33965584 / 100000000 * (33965584 / 100000000) = 1153660896461056 / 10000000000000000")
                                                                                                                                                                  (("1"
                                                                                                                                                                    (hide
                                                                                                                                                                     -1)
                                                                                                                                                                    (("1"
                                                                                                                                                                      (replace
                                                                                                                                                                       -4)
                                                                                                                                                                      (("1"
                                                                                                                                                                        (inst-cp
                                                                                                                                                                         -
                                                                                                                                                                         "2"
                                                                                                                                                                         "3")
                                                                                                                                                                        (("1"
                                                                                                                                                                          (replace
                                                                                                                                                                           -2)
                                                                                                                                                                          (("1"
                                                                                                                                                                            (replace
                                                                                                                                                                             -6)
                                                                                                                                                                            (("1"
                                                                                                                                                                              (case-replace
                                                                                                                                                                               "33965584 / 100000000 * (197951423552 / 1000000000000) = 6723535704575034368/100000000000000000000")
                                                                                                                                                                              (("1"
                                                                                                                                                                                (replace
                                                                                                                                                                                 -5)
                                                                                                                                                                                (("1"
                                                                                                                                                                                  (hide
                                                                                                                                                                                   -1)
                                                                                                                                                                                  (("1"
                                                                                                                                                                                    (inst-cp
                                                                                                                                                                                     -
                                                                                                                                                                                     "3"
                                                                                                                                                                                     "3")
                                                                                                                                                                                    (("1"
                                                                                                                                                                                      (replace
                                                                                                                                                                                       -7)
                                                                                                                                                                                      (("1"
                                                                                                                                                                                        (case-replace
                                                                                                                                                                                         "197951423552 / 1000000000000 * (197951423552 / 1000000000000) = 39184766086263300296704/1000000000000000000000000")
                                                                                                                                                                                        (("1"
                                                                                                                                                                                          (hide
                                                                                                                                                                                           -1)
                                                                                                                                                                                          (("1"
                                                                                                                                                                                            (replace
                                                                                                                                                                                             -4)
                                                                                                                                                                                            (("1"
                                                                                                                                                                                              (simplify
                                                                                                                                                                                               -4)
                                                                                                                                                                                              (("1"
                                                                                                                                                                                                (simplify
                                                                                                                                                                                                 -5)
                                                                                                                                                                                                (("1"
                                                                                                                                                                                                  (simplify
                                                                                                                                                                                                   -6)
                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                    (simplify
                                                                                                                                                                                                     -7)
                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                      (inst-cp
                                                                                                                                                                                                       -
                                                                                                                                                                                                       "3"
                                                                                                                                                                                                       "4")
                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                        (replace
                                                                                                                                                                                                         -8)
                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                          (replace
                                                                                                                                                                                                           -7)
                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                            (simplify
                                                                                                                                                                                                             -4)
                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                              (replace
                                                                                                                                                                                                               -4)
                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                (hide
                                                                                                                                                                                                                 -9)
                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                  (inst-cp
                                                                                                                                                                                                                   -
                                                                                                                                                                                                                   "4"
                                                                                                                                                                                                                   "4")
                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                     -8)
                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                       -4)
                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                        (inst-cp
                                                                                                                                                                                                                         -
                                                                                                                                                                                                                         "4"
                                                                                                                                                                                                                         "5")
                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                           -8)
                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                             -9)
                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                              (replace
                                                                                                                                                                                                                               -4)
                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                (inst-cp
                                                                                                                                                                                                                                 -
                                                                                                                                                                                                                                 "5"
                                                                                                                                                                                                                                 "5")
                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                   -9)
                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                                     -4)
                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                      (inst-cp
                                                                                                                                                                                                                                       -
                                                                                                                                                                                                                                       "5"
                                                                                                                                                                                                                                       "6")
                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                         -9)
                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                           -10)
                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                             -4)
                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                              (inst-cp
                                                                                                                                                                                                                                               -
                                                                                                                                                                                                                                               "6"
                                                                                                                                                                                                                                               "6")
                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                                                 -10)
                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                                   -4)
                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                    (case-replace
                                                                                                                                                                                                                                                     "(197951423552 / 1000000000000 *
          (1153660896461056 / 10000000000000000)) = 228368816750742514129190912/10000000000000000000000000000")
                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                      (hide
                                                                                                                                                                                                                                                       -1)
                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                        (inst-cp
                                                                                                                                                                                                                                                         -
                                                                                                                                                                                                                                                         "6"
                                                                                                                                                                                                                                                         "7")
                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                                           -10)
                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                                             -11)
                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                              (replace
                                                                                                                                                                                                                                                               -4)
                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                (inst-cp
                                                                                                                                                                                                                                                                 -
                                                                                                                                                                                                                                                                 "7"
                                                                                                                                                                                                                                                                 "7")
                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                                                   -11)
                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                                                                     -4)
                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                      (inst-cp
                                                                                                                                                                                                                                                                       -
                                                                                                                                                                                                                                                                       "7"
                                                                                                                                                                                                                                                                       "8")
                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                                                         -12)
                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                                                           -11)
                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                            (replace
                                                                                                                                                                                                                                                                             -4)
                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                              (inst-cp
                                                                                                                                                                                                                                                                               -
                                                                                                                                                                                                                                                                               "8"
                                                                                                                                                                                                                                                                               "8")
                                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                                                                                 -12)
                                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                                  (replace
                                                                                                                                                                                                                                                                                   -4)
                                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                                    (inst-cp
                                                                                                                                                                                                                                                                                     -
                                                                                                                                                                                                                                                                                     "8"
                                                                                                                                                                                                                                                                                     "9")
                                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                                                                                       -12)
                                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                                                                         -13)
                                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                                          (replace
                                                                                                                                                                                                                                                                                           -4)
                                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                                            (inst-cp
                                                                                                                                                                                                                                                                                             -
                                                                                                                                                                                                                                                                                             "9"
                                                                                                                                                                                                                                                                                             "9")
                                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                                              (replace
                                                                                                                                                                                                                                                                                               -13)
                                                                                                                                                                                                                                                                                              (("1"
                                                                                                                                                                                                                                                                                                (replace
                                                                                                                                                                                                                                                                                                 -4)
                                                                                                                                                                                                                                                                                                (("1"
                                                                                                                                                                                                                                                                                                  (inst
                                                                                                                                                                                                                                                                                                   -
                                                                                                                                                                                                                                                                                                   "9"
                                                                                                                                                                                                                                                                                                   "10")
                                                                                                                                                                                                                                                                                                  (("1"
                                                                                                                                                                                                                                                                                                    (replace
                                                                                                                                                                                                                                                                                                     -12)
                                                                                                                                                                                                                                                                                                    (("1"
                                                                                                                                                                                                                                                                                                      (replace
                                                                                                                                                                                                                                                                                                       -13)
                                                                                                                                                                                                                                                                                                      (("1"
                                                                                                                                                                                                                                                                                                        (replace
                                                                                                                                                                                                                                                                                                         -3)
                                                                                                                                                                                                                                                                                                        (("1"
                                                                                                                                                                                                                                                                                                          (hide-all-but
                                                                                                                                                                                                                                                                                                           (-20
                                                                                                                                                                                                                                                                                                            -21
                                                                                                                                                                                                                                                                                                            1))
                                                                                                                                                                                                                                                                                                          (("1"
                                                                                                                                                                                                                                                                                                            (expand
                                                                                                                                                                                                                                                                                                             "abs"
                                                                                                                                                                                                                                                                                                             -2)
                                                                                                                                                                                                                                                                                                            (("1"
                                                                                                                                                                                                                                                                                                              (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)
                                                                                                                                                                                                                                                     ("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)
                                                                                                                                                                                         ("2"
                                                                                                                                                                                          (assert)
                                                                                                                                                                                          nil
                                                                                                                                                                                          nil))
                                                                                                                                                                                        nil))
                                                                                                                                                                                      nil))
                                                                                                                                                                                    nil))
                                                                                                                                                                                  nil))
                                                                                                                                                                                nil)
                                                                                                                                                                               ("2"
                                                                                                                                                                                (assert)
                                                                                                                                                                                nil
                                                                                                                                                                                nil))
                                                                                                                                                                              nil))
                                                                                                                                                                            nil))
                                                                                                                                                                          nil))
                                                                                                                                                                        nil))
                                                                                                                                                                      nil))
                                                                                                                                                                    nil)
                                                                                                                                                                   ("2"
                                                                                                                                                                    (assert)
                                                                                                                                                                    nil
                                                                                                                                                                    nil))
                                                                                                                                                                  nil))
                                                                                                                                                                nil))
                                                                                                                                                              nil))
                                                                                                                                                            nil)
                                                                                                                                                           ("2"
                                                                                                                                                            (assert)
                                                                                                                                                            nil
                                                                                                                                                            nil))
                                                                                                                                                          nil))
                                                                                                                                                        nil))
                                                                                                                                                      nil))
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil)
                                                                                                                                           ("2"
                                                                                                                                            (expand
                                                                                                                                             "^"
                                                                                                                                             1)
                                                                                                                                            (("2"
                                                                                                                                              (expand
                                                                                                                                               "expt")
                                                                                                                                              (("2"
                                                                                                                                                (expand
                                                                                                                                                 "expt")
                                                                                                                                                (("2"
                                                                                                                                                  (expand
                                                                                                                                                   "expt")
                                                                                                                                                  (("2"
                                                                                                                                                    (assert)
                                                                                                                                                    nil
                                                                                                                                                    nil))
                                                                                                                                                  nil))
                                                                                                                                                nil))
                                                                                                                                              nil))
                                                                                                                                            nil))
                                                                                                                                          nil))
                                                                                                                                        nil))
                                                                                                                                      nil))
                                                                                                                                    nil))
                                                                                                                                  nil)
                                                                                                                                 ("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"
                                                                                    (assert)
                                                                                    nil
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil)
                                                                         ("2"
                                                                          (hide-all-but
                                                                           1)
                                                                          (("2"
                                                                            (expand
                                                                             "^")
                                                                            (("2"
                                                                              (expand
                                                                               "expt")
                                                                              (("2"
                                                                                (expand
                                                                                 "expt")
                                                                                (("2"
                                                                                  (expand
                                                                                   "expt")
                                                                                  (("2"
                                                                                    (expand
                                                                                     "expt")
                                                                                    (("2"
                                                                                      (expand
                                                                                       "expt")
                                                                                      (("2"
                                                                                        (expand
                                                                                         "expt")
                                                                                        (("2"
                                                                                          (assert)
                                                                                          nil
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil)
                                                                     ("2"
                                                                      (hide-all-but
                                                                       1)
                                                                      (("2"
                                                                        (assert)
                                                                        nil
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil)
                                                               ("2"
                                                                (hide-all-but
                                                                 1)
                                                                (("2"
                                                                  (grind)
                                                                  nil
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2" (assertnil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (assertnil nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((ln_strict_increasing formula-decl nil ln_exp nil)
    (sigma def-decl "real" sigma "reals/")
    (strict_decreasing? const-decl "bool" real_fun_preds "reals/")
    (+ const-decl "[T -> real]" real_fun_ops "reals/")
    (const_fun const-decl "[T -> real]" real_fun_ops "reals/")
    (ln const-decl "real" ln_exp nil)
    (ln_1 formula-decl nil ln_exp nil)
    (strict_increasing? const-decl "bool" real_fun_preds "reals/"))
   shostak))
 (ln_ineq4 0
  (ln_ineq4-1 nil 3254161830
   ("" (skosimp*)
    (("" (lemma "ln_ineq1" ("xgtm1" "px!1-1"))
      (("1" (flatten) (("1" (assertnil nil)) nil)
       ("2" (assert)
        (("2" (case "px!1=1")
          (("1" (replace -1 2)
            (("1" (rewrite "ln_1") (("1" (assertnil nil)) nil)) nil)
           ("2" (assertnil nil))
          nil))
        nil))
      nil))
    nil)
   ((posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (nzreal_gt_m1 nonempty-type-eq-decl nil ln_exp_ineq nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (> const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (/= const-decl "boolean" notequal 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)
--> --------------------

--> maximum size reached

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

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

¤ Dauer der Verarbeitung: 0.547 Sekunden  (vorverarbeitet am  2026-04-28) ¤

*© Formatika GbR, Deutschland






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Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.