Quelle  convex_functions.prf   Sprache: Lisp

(convex_functions
 (composition_of_convex 0
  (composition_of_convex-1 nil 3465141264
   ("" (skeep)
    (("" (expand "convex?")
      (("" (skeep)
        (("" (expand "o")
          (("" (inst -2 "x" "y" "t")
            (("" (assert)
              ((""
                (inst - "f(t * x - t * y + y)"
                 "f(y) - t * f(y) + t * f(x)")
                (("" (assert)
                  (("" (inst - "f(x)" "f(y)" "t")
                    (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions nil)
    (O const-decl "T3" function_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real nonempty-type-from-decl nil reals nil)
    vex_functions
    (number_field nonempty-type-from-decl
    ( const-decl "number > boolean]" number_fields
     nil)
    (boolean  nil booleansnil)
    (number nonempty-type-decl 
   nil))
 (max_of_convex 0
  (max_of_convex-1 nil 3462698433
   ("" (skeep)
    (("" (expand "convex?")
      (("" (skeep)
        (("" (inst?)
          (" (inst?
            (("" (assert)
              ((" ( -3)
                (("" (hide -3)
                  ((""
                    (case "f(t * x - t * y (inst - ""ft * x t y +y"
                    (("1 ("  (composition_of_convex-1 346416java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
("( - f(x)"() t"java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
                         )
                          " expand max"(1assertnil)
                            )java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
                            -numfield" nil
                            ( assert( application-judgement" nil)
                              (("2"
( - "(1-d]" )
                                (("2"
                                  (mult-by -3 "t")
                                  (" (assertnil ))
                                  nil))
                                nil)
                              
                            numfield nonempty-type-eq-decl nil )
 expandmax)
                            (("3" (assert)
                              (("3"
                                (mult-by2 "1-t))
                                (("3"
                                  (mult-by -3 "t")
(("3" (assert) nil nil))
                                  nil    (*    numbersnil)java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
nil
                              nil))
                )
                           ("4" (expandnumbernonempty-type-decl nil  nil)
                            (("4" (assert)
                              ""(?)
                                mult-by2"java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 22
                                ((" ("" assert)
                            "java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
            (4 y ) = gt *  *  +y orf(  x-t  y y<gt* -t   +))
nil)java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
                                )
                              nil))
                                          (""                          (" ((expand max (("1 assert nil nil))
                           (assert)
                              (5
                                 -1)java.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
                                6
                                  ((mult-byjava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                                  (("5" (assertnil
                                  nil))
                                nil)                              (7
                              ( - t"java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
                            nil)
                           ("" "max")
                            (("nil)
                              (("6"
mult-by2 "1t))
                                (("6"
( 3")
                                  (("6" (assert) nil nil))
                                  ( (   
                                ))
                              nil))
                            nil)
                           ("7" (expand nil)
                            (("7" (assert)
                              ((2"(1 (2" ) )java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
                                nil
                                ((        )java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
                                  (mult-by -3  nil)
                                  (("7" (assert) nil nil))
                                  nil(number nilnumbersnil)
nil
                              nil))
                            nil)
                           ""( ")("8"(assert) niljava.lang.StringIndexOutOfBoundsException: Range [69, 66) out of bounds for length 71
                            nil)( "[ ->boolean"  java.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
                          nil)
                         ""  il
                          (("2"     
                            (("2" (grindnil
                          nil)
                        nil)
                       ("2" (hide-all-but     real_ge_is_total_order name-judgement"(otal_order?real])"
                        nil))
    (maxconst-decl"{: real p> m AND p > n} niljava.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
                     ("2" (real_lt_is_strict_total_ordername-judgement
                )
                         nil)
                  ))
                     real_props nil
          )java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
    (bot formula-declnil( boolreals)
          nil    (  java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 9
        nil))
)
l
   ("strict_total_order?real)"real_props)
tion-judgement"" realsnil
java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 35
    (*"numfield,numfield->]"number_fieldsnil)
    ( nil    OR ,java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 55
    (number_field_pred const-decl "[ -> ]"number_fields
     nil)
    (number_field    (numfield nonempty-type-eq-decl il   shostak))
    (real_pred const-decl 1190
    (realeep)
    *"numfield - numfield]number_fields)
     real_props nil)
    (  nilextra_real_props
     nil)
     name-judgement
     real_minus_real_is_real    (real_minus_real_is_real 
    (real_ge_is_total_order name-judgement "(total_order?[real])"
      )
    (max const-decl "{p: real nil))
nonempty-type-eq-decl real_typesnil
    (both_sides_times_pos_ge1_imp formula-decl java.lang.StringIndexOutOfBoundsException: Range [0, 50) out of bounds for length 11
niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    posreal  nil)
    (> const-decl "bool" reals(real_plus_real_is_real application-judgement ""  )
    (both_sides_times_pos_lt1 formula-decl nil real_props nilnil)
    (bool            nil nil numbersniljava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
    (OR    (  "number - ]" number_fields
    (=  " nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (+ ( "number_field >boolean"  ( realreals)
         nilrealsnil)
*"[is_real "realrealsnil
    (< (eal_le_is_total_order name-judgement( const-decl"" convex_functions niljava.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
    ))
   shostak))
 ( 0
  (sum_of_convex-1 nil 34  scal_convex-1 45143177
   ("" (skeep nonempty-type-from-decl nil nil
    (" ( " skeep)
      (((" expand "convex?")
        (("(inst - (""(skeepjava.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
          ( name-judgement"(?real)
            (""(ssert
              ((""     (+ const-decl"T - " java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
            nil))
          nil))
        ))
      nil))
    nil)
   ((   ( application-judgementreal reals)
    (real_plus_real_is_real application-judgement "real (("inst- x""y t)
    (?  "" convex_functionsnil
    (number nonempty-type-declconvex  bool   (")
    boolean( mult-by-aaa)((  il) )java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
    number_field_pred nil
nil)
    ((    nil)
    (real_pred const-decl "[number_field - application-judgement "nil
     real_propsnil)
    (  rreals nil
    (java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 9
real_propsnil)
(+[- eal real_fun_opsnil)
   shostak))
 scal_convex 00
  (scal_convex-1 nil 3465142    (bool nonempty-type-eq-declnil  )
   ("" (skeep)
" expand"convex( nonempty-type-decl nilbooleans)
      (""skeep
        (("" (inst -+ "numfield,n -]" umber_fields
      (" (expand*)
            (("" (assert)
(("factorjava.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
                " mult-by 1 aaa" " (" (nil)
    real  nil realsniljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48

     nil
          nil))
nil)
      nil))
    nil
   ((real_times_real_is_real application-judgement     )
    (real_plus_real_is_real application-judgement "real reals nil) nonempty-type-from-decl number_fields nil)
    (    real_predconst-decl"number_field iljava.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
    (    bool nonempty-type-eq-declnilbooleans name-judgement
    (  booleans)
    (number_field_pred const-decl  -const-decl "numfield,numfield -numfield ( (convex? "")
     )
    (number_field nonempty-type-from-decl nil number_fields nil)
    ( const-decl "number_field >boolean ( application-judgement real reals nil)
    real  nil reals nil
    real_minus_real_is_real real=[T- "n
( "total_order[real)
     real_props nilconvex_function_right_lt-3nil 509java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
    (both_sides_times_pos_le1_imp(booleannonempty-type-decl nilbooleans   " """java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
     iljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (nnreal("" inst BAtt)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields                (1 ( " + numbers)
    (- const-decl "[numfield (number_field_pred const-decl ""()
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl( nonempty-type-from-declniljava.lang.StringIndexOutOfBoundsException: Range [46, 39) out of bounds for length 39
    =("java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
]  ))
   shostak))
(convex_function_right_lt_TCC1 
  (convex_function_right_lt_TCC1-1strict_total_orderrealreal_propsnil)
   ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool (""
    (NOT const-decl "[bool (replace "ttname"
( nonempty-type-decl numbersnil
    (number_field_pred const-decl [ -> boolean]"number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
il
    (real_minus_real_is_real application-judgement "real" reals nil)
    real_lt_is_strict_total_ordername-judgement
     "(strict_total_order?[real (convex_function_right_lt 0
    (convex?const-declnililjava.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
 niljava.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
    real_times_real_is_realapplication-judgement  reals nil
    (real_plus_real_is_real application-judgement "real" reals("" labelottname -1)
   nil" cross-mult )
 (""(fieldnil nil) nil))
  ( nil3463
   ("" (skeep)
    (("" (name "tt" "(C-A)/(B-A)" ((2( "ttname" +rl
      (("1"                  (" ((2 cross-mult1)("2(assert)nil )
        (("1" (case "1-tt = (B-C)/(B-A)")
          (("1" (label "ottname" -1)
            (("1" (expand "convex?")
              (("1" (inst 3 ("ttname+java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 53
(("1"nil)
                  (("1" (replace -1)
                    ("
                      (("1" (split)
                        (nil
                          (case-replace
                           ))nil
                          (("1"
                            ((""
                            ((()
                              (("1 nil)
(replace ttname+ l)
                                (("1"
                                  (cross-mult 1)
                                                     (        java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
                                  nil))
                                )
                              nil)
                             "" ((cross-mult1
                              (    (nznumnonempty-type-eq-declnil number_fieldsnil)
                            nil)
                           (( number_fields"(1nil )nil)
)nil))
     T  >] n(2replacettname +rl)
(2(nonempty-type-decl booleans niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
                          (("2" (nil
                            nil))
                          nil)
                         " (replacettname rl
                          (("3" (cross-mult 1) (("3 (("3" (cross-multreal_times_real_is_realapplication-judgement "  )
                            nil))
))
                        nil))
                      nil)
                    nil)
                   ("2" (replace "ttname" + rl)
                    (("2" (field 1) nil nil)) nil))
                  )java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
                nil)nil)
              nil))
           niljava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
           ("2" (replace "ttname" + rl) (("2" (field 1) nil nil(" replace ttname" +rl ("2 (field 1) nil nil)) nil))
          nil))
        nil)
       ""(   nonzero_realnonempty-type-eq-declnileals)
      nil)
   nilnil(bool  nil booleansnil)
-nilreals niljava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    - const-decl"numfield,numfield>numfield]"number_fieldsniljava.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (/ const-decl "[numfield, nznum ->(/= const-decl "boolean" notequal n)
    ( nonempty-type-from-decl nil number_fields nil)
(=const-decl "boolean" notequal nil
    (number_field nonempty-type-from-decl nil number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil
    (number_field_pred const-decl "[number -> boolean]" number_fields
     =const-decl [T  -boolean]"equalities ) (? ""functions java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
    =[ T- ]" equalities nil)
    booleannonempty-type-decl nil niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    ( nonempty-type-decl nilnumbersnil)
     (real_minus_real_is_real application-judgement "real"realsnil)
    (real_minus_real_is_real application-judspan style='color:blue'>",T- ( nil booleans)
    numbernonempty-type-decl   nil
    real_minus_real_is_realapplication-judgementreal  nil
    real_times_real_is_real ""realsnil)
    (    (real_plus_real_is_real "reals iljava.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
convex?ealnonempty-type-eq-decl  nil
    +const-declnumfield] java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (* const-decl "[numfield, numfield -> numfield]"     (div_mult_pos_gt1 formula-decl nil extra_real_props nil
    (real_le_is_total_order name-judgement "(total_order?[real])"
      nil)
    name-judgement"total_order?[eal]
     real_props nil)
    (real_lt_is_strict_total_order nil
     "(strict_total_order?[real])" real_props nil)
    (div_mult_pos_le1 formula-decl nil real_props nil)
java.lang.StringIndexOutOfBoundsException: Range [21, 4) out of bounds for length 54
    ((times_div2formula-decl nil)"( " (/)"java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
      ("onst-decl"  ]booleansnil
    ( formula-declnil real_propsnil    (const-declbool nil
(nonzero_real nonempty-type-eq-decl   nil
(    ("1 expand "?)
    (bool nonempty-type-eq-decl nil booleans nil)
    (> const-decl "bool" reals nil)
    (both_sides_times_pos_ge1 formula-decl nil real_props nil)
    nonneg_realnonempty-type-eq-decl(onneg_realnonempty-type-eq-decl eal_typesniljava.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
    (posreal nonempty-type-eq-decl nil real_types nil)
    (FDX_65 skolem-const-decl "real"    > const-decl " ssertjava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 34
    (>= const-decl "bool" reals nil)
((strict_total_order?[real real_props nil)
 name-judgement
     "(strict_total_order?[real])" real_props nil)
       (  bool functionsjava.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 48
    (id const-decl "(bijective (TRUE const-decl bool"booleansnil
    (TRUE const-decl "bool" booleans nil)
    both_sides_times_neg_ge1  eal_props )
    (nonpos_real nonempty-type-eq-decl((""
    (negreal nonempty-type-eq-decl nil real_types nil
    (< const-decl "bool" reals nil) (<= const-decl "bool" reals nil)
    (div_mult_pos_gt1 formula-decl                                   assert) nil))))java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
( application-judgement"
     real_types nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (both_sides_times1formula-declnilreal_props )
   nil)
  convex_function_right_lt-23504
   ("" (skeep)
    (("" (name (both_sides_times1nil)
      (("1" (labelconvex_function_right_lt-2 45086
        (""        )
          (1 (ottname 1
            label""-)
                            ("3" assert)))))))
((java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
                  1 replace1java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
                    (("1" (assert1)
                      (("1" (splitt)
                        ("1"
                          (
                           "(B (""("" split)
                          (("1"
                            (case-replace(("1"
                             "( - C /C A) (-)t"
                              (("1"
                                 "" + rl
                                (1
                                  (("1"()nil)))
                                  (("1" (assert) nil)))))))
(2 cross-mult)
                              (("2" (assert) nil)))))
                           ("2" (cross-mult 1) (("2" (field 1) nil)))))
                         ("2" (replace "ttname" + rl)
 )(2"()java.lang.StringIndexOutOfBoundsException: Range [65, 63) out of bounds for length 70
                         ("3" (replace "("" ce "" +)
                          (3 ( 1)
                            (("3" (ssertnil)))))
                   ("3 replace"tname       " assert) nil))java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
                    ""f ) )))))
           ("2" (replace "ttname" + rl      (("1"       (("1" (label("()))))java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
       ("2" (assert) nil))))

   nil nil)
  (convex_function_right_lt-1 nil 3465305687
( skeep
    ("2( -java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
      (("1" (label "tname" -1)
        (("1" (case " nil nil))
("""java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
            (("1" (expand                          (1
              (("1" (inst - "B" " ("()(""( )
                (("1" (case "A + t * B - t * A ( nonempty-type-eq-decl nil nil)
                  (("1"     (NOT                              "
                    (("1" (assert)
                      (1 (n nil
                        (1sp; (("1" (case "1-t = (B-C)/ ((""
          (("1" (label "otname" -1)
(1"(expand "convex?)
              (("1" (inst - "B" "A" "t")
                (("1" (((""
-
                    "(assertjava.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
("1(splitjava.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
                        1
ase-replace( )/( -A) =(1t/"
("1"
                            (case-replace "(B - A) / (C - A) = 1/t")
                            (("1" (field 1)
((""
                                (replace "tname" +                              
                                (("1"
                                (""
                                  (1" assert )))))java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                             ("2""3"  "2(1java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
                              (("2" (assert) nil)))))
                          2 (                           ("2" (cross-mult"2 assert nil))java.lang.StringIndexOutOfBoundsException: Index 70 out of bounds for length 70
                        2  "ttname +rl)
                          (("2" (cross-mult 1) (("2" (assert) nil                          (("3(cross-mult
                         "( "tname"("assert)java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
"( (" ( 1 )))))java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
(" assert )))))java.lang.StringIndexOutOfBoundsException: Index 57 out of bounds for length 57
                   "2 (replace "tname+rl
                    (("2" (field(""java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 8
           ("2"   (" ()
       (""       ("2" (1"inst-B"A t"java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
    nil)
   nil))
 (convex_function_left_lt_TCC1 0          ((1         ("
  convex_function_left_lt_TCC1-13463058java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
   " subtype-tcc nil (" field1
   ((boolean nonempty-type-decl nil booleans nil)
    boolnonempty-type-eq-decl booleansniljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
( const-decl(("1java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
  )
    (number_field_pred const-decl "[number - ((1"
    nil
    (number_field nonempty-type-from-decan style='color:red'>nil))
    nil)
   ((real_div_nzreal_is_real application-judgement "real (bool nonempty-type-eq-decl nil booleansniljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    minus_odd_is_odd "odd_int" integers    numfieldnonempty-type-eq-declnil 
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
real_props)
    real_lt_is_strict_total_order
     (?nil
    (bool    nznumnonempty-type-eq-decl nilnumber_fields)
    (NOT const-decl "[bool -TRUEconst-decl bool"booleans)
    / const-decl ""  nil)
(    (convex_function_right_lt nilconvex_functions nil)java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
  ( nil3     strict_total_orderreal)real_props java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
    (= const-decl      ("1"  (DX_69r  java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
* [,numfield- ]number_fieldsn)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum- numfield"  nil
(  ""booleans("((3()nil nil)nil)java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
nil
    (bijective? const-decl "bool" functions nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (>= const-decl "bool" reals nil    niljava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
"" )
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
     nil)
    ( nonempty-type-from-decl       nil)
    ( name-judgement(otal_order    (nonempty-type-declnilnumbersjava.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
 td_av
    div_mult_pos_ge2  nil
    (""( x = y")
times_div2formula-decl)
    (> const-decl "bool" reals nil    (real_le_is_total_ordername-judgement "total_order?real]
(  "java.lang.StringIndexOutOfBoundsException: Range [62, 52) out of bounds for length 67
nonempty-type-from-decl reals)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
number_field_pred  [ -> boolean]" number_fields
     nil)
booleannonempty-type-decl nilbooleansnil)
       n"total_order[]"
    (convex_function_right_lt formula-decl nil convex_functions nil))
   shostak))
 between_point_is_wtd_av0

   ("" (skeep)
    (("" (case "x = y")        nil)
      ""inst+ ("1assert) )
       ("2" (inst + "(y-z)/(y-x)")
        (("1" (prop)
(1"(1)( (onneg_real nonempty-type-eq-decl nil real_types nil)
"2 (ross-mult 1) (" () nil))niljava.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
       ("( "()") ((java.lang.StringIndexOutOfBoundsException: Range [9, 6) out of bounds for length 9
          nil)
         (2 () nil booleansniljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
        nil))
      nil)
nilNOT"bool" il
   ((real nonempty-type-from-decl const-decl[,numfield-numfield" number_fieldsnjava.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (real_predconst-decl"[number_field- boolean]"  nil
        real_le_is_total_ordernonzero_real nil )
eal_propsjabsp;  ("1" (ross-mult 1)("" assertnilnil)) nil    real   nilreals java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
           (    (number_field_pred const-decl"numberjava.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
           ("3" (mult-by 1 "(y-x)") (("3" (field)     (numbernonempty-type-decl nil    real_ge_is_total_orderame-judgement "?"
          nil)
         ("2" (assert) nil nil)    >  (between_point_is_wtd_av-1 nil42721
        ))
      nil))
    nil      (" (+ 0)((1 ( nil)niljava.lang.StringIndexOutOfBoundsException: Index 52 out of bounds for length 52
          ("1 cross-mult 1) ((java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 58
    (real_pred const-decl "[number_field -> boolean]" reals nil)
        (div_mult_pos_le1 formula-decl
    (number_field_pred const-decl "[number -> boolean]" number_fields
nil
    (= const-decl "[T, T -> boolean]" equalities    (bijective? const-decl "" functionsnil
type-decl booleans java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
    (number nonempty-type-decl nil numbers     nil( const-decl"bool >bool] niljava.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
(    nonempty-type-eq-declnilrealsnil)
     eal_propsniljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
    real_times_real_is_realnil umber_fields)
    (  nil  niljava.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
     "(strict_total_order?[real])" real_props nil)
_order?[[])"
     real_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
AND "[ - bool]"booleans niljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
    (>= const-decl "bool" reals nil) (> const-decl "bool" reals( name-judgement
    (posreal nonempty-type-eq-decl nil real_types nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    div_mult_pos_le2 formula-declnilrnil
    (div_mult_pos_le1 formula-decl nilreal_props)
umfield" number_fields niljava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
    (bijective? const-decl "bool" functions nil)
    (id const-decl(= const-decl      ("(inst ""java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 31
    (TRUE const-decl "bool" booleans nil)
    (minus_odd_is_odd  "odd_int" integers nil)
    (NOT const-decl "[bool -> bool (("" (inst + "(1-t!1)"(div_mult_pos_le2 nilreal_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    +onst-declnumfield,numfield->numfield" number_fields niljava.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
    (nonzero_real nonempty-type-eq-decl nil     nil) const-decl"bijective[,T)"identityniljava.lang.StringIndexOutOfBoundsException: Index 53 out of bounds for length 53
    (both_sides_times1 formula-decl nil real_props nil)
    (  "numfield,, znum -> numfield]" number_fieldsnil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (  nil number_fields"[number_field -> boolean]" reals nil)
    (number_field java.lang.StringIndexOutOfBoundsException: Range [32, 24) out of bounds for length 40
lean"java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
     nil)
    (boolean                  (1 (eplace)
                    (1 label"1)
                      (1 inst "!"
 (onvex_const_on_connected_min
  (convex_const_on_connected_min-1 nil 34628(")java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
   ("" (skosimp*)
                               "" "!(!)+tt*f!(!)
      (("1" (expand "convex?")
        " ( "ttt""!-                           )java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
          (("1 label""-java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
            (("1" (inst - "w!1" "x!1"                    2 (replace(""
              ((((2  ("
                (""( "x1+ttt *!1- * x1=y1"
                  " assert )java.lang.StringIndexOutOfBoundsException: Index 62 out of bounds for length 62
"1)
                      (("1" (inst - "y!1")
                        ("(assert)java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
                          (("1" (replace))
                            nil)
                              (both-sides "-" "f!1(x!1)+ttt*f!1(x!1)"
                               )
                              "1
                                                    ( (hide-all-but1
                                "
                        ""()
        (""
                                                              )java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
                                    1
                                      )
                                      (("1" (assert) nil nil))
                                      nil))
                                    nil))
                                  )
                                nil          ((1                  "(replace"ame+)
                              nil))
                            )
                          nil))
                        nil))
                      nil))
                   nil
                   ("( "  java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
                    (("2"(""  "1java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
          ((1assert
            ("assertjava.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
                         "both-sides"ttt!x1 )
                          nil))
                        )
                                                        (""(case w1    -tt w1 !)
                    )
nil
                 (""()
                  ((""( - -rl)
                  nil)
                 ("3"("" +rl
                  (3 cross-mult1 (" ((1
                  nil))
                nil))
              nil))
            nil)
           (("1
          nil))
            ( -)
       ("2"(("java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 41
        (("1" expand convex"java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
          (1( "ttt" "x1-!)/(!-!))
            (("1" (label "tname" -1)
              (("1" (inst -(("1"
                (("1" (                                              ( 3""java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 59
                  (1 case((2"
                    (("" (replace 1java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
                      nil
                        (("1" (inst - "y!1")
                                                                       ("

                             sp;(""(("(replace ""+ java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
            (("1" (nil)
              (("1" (inst)
                (("1" (prop)
                  (("nil)
                    (("1" (replace -                   2 replace"name"+)
                      (("1" (label "xname" -1)
                        (1"""(asejava.lang.StringIndexOutOfBoundsException: Range [20, 18) out of bounds for length 30
                          (("()
                            ((            (2()
                              (("1"
both-sides"""tttf(!" 2
                                (("1"
                                  
(                  w+ttty! -tt w=x!"java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
                                    (factor -2)
                                    (("1"
                                      (name "GEE" "(1-ttt)"java.lang.StringIndexOutOfBoundsException: Index 59 out of bounds for length 44
                                      (("1"
                 "3 replace tname )
                                        (""( )( (("java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
                                          (div-by -3 "GEE")
                                          (("1"
                                            ( GEE"1-))
                                            " (expand"?)
                                             (                                        " java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 50
                                              div-by-"EE)
                                              (("2"
                                                (cross-mult 1)
                                                ""
                                                                      (1 replace-)
                                                  
                                                  nil                                                  (2
                                              2
                                              nil)
                                            
                                          
                                        nil))
                                      nil)
                                    nil))
                                  nil)                                              nil))
                                nil))
                              nil))nil))
                            nil))
                          )java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
                        nil))
                      nil)
                     ("2" nil                                   java.lang.StringIndexOutOfBoundsException: Range [64, 63) out of bounds for length 68
                      (("2" (mult-by 1 "(y!1 - w!1)")
                        (("2" (field 1) nil nil))                                                   (as
                      nil))
                    nil)
                   ("2" (replace "tname" + rl)
                    (("2" (cross-mult 1) (("2" (assert) nil nil)) nil))
                    nil)
                   (                                          )
                    (("3" nil)""(replace"name"+)
                    )                    ""( )(2 assertnilnil nil)
                  nil))
                nil))
              nil)
             ("2" (assert) nil nil))
            nil))

(2 (inst w1) (""(  nil)nil)
        nil))
      nil))
    nil)
   ((>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans 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 " ((2 cross-mult1 ""()n nil))
     nil)
    boolean nilbooleansnil))nil
    (number nonempty-type-decl((" cross-mult 1)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (= const-decl "[T, T( nilr
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (/                  (al_predconst-decl number_field- niljava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
    nznumnonempty-type-eq-decl nil
    number  numbersnil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields(""( -"!" (a ""  java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 68
    (div_mult_pos_le1 java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 8
    (AND const-decl "[bool, bool ->( nilrealsnil)
eal_pred  number_field>boolean]"realsniljava.lang.StringIndexOutOfBoundsException: Index 64 out of bounds for length 64
    x!skolem-const-declrealconvex_functionsnil
    (div_mult_pos_le2 formula-decl nil real_props nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields java.lang.StringIndexOutOfBoundsException: Index 68 out of bounds for length 56
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    ((div_mult_pos_le2 nil " )
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (<= const-decl "bool" reals nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (both_sides_minus_le1 formula-decl nil real_props nil)
    (both_sides_plus_le2 formula-decl nil real_props nil)
    ( java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
     "(strict_total_order?[real])" real_props nil)
    ( const-decl "bool" reals nil)
    ( application-judgement ""
     real_types nil)
    ( formula-declnil java.lang.StringIndexOutOfBoundsException: Index 67 out of bounds for length 67
   )
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (CBD_77 skolem-const-decl "real" convex_functions nil)
    bijectiveconst-decl bool )
    (id const-decl "(bijective?[T, T])" identity nil)
    (TRUEconst-decl boolbooleansnil
    (minus_even_is_even application-judgement "even_int" integers nil)
java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
    (zero_times1 formula-decl nil real_props nil)
    (div_mult_pos_ge1 formula-decl nil real_props nil)
    (nonpos_real nonempty-type-eq-decl nil real_types nil)
    (both_sides_times_neg_le1_imp formula-decl nil extra_real_propsnil(=const-decl oolreals)
     niljava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
    (div_mult_neg_le1 formula-decl nil real_props)
 application-judgementrealreals )
    (neg_one_times formula-decl nil extra_tegies nil)
    (div_mult_pos_gt1 formula-decl nil extra_real_props         (minus_evens_even application-judgementeven_intintegers)
    ( nonempty-type-eq-decl( formula-decl extra_real_props
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (nonzero_real nonempty-type-eq-decl nil reals nil)
( nilreal_propsnil
    (convex? const-decl "bool" convex_functions nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (both_sides_div_pos_le1 formula-decl nil real_props nil)
GEEskolem-const-declreal n real_types)
    (formula-declnil extra_real_props)
    (div_mult_pos_lt1 formula-decl nil( nonempty-type-eq-declnil  java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
    (y!1 skolem-const-decl "real" convex_functions nil)
    (< const-decl "bool" reals nil))
   shostak))
 ( 0
  (convex_min_is_connected-1 nil 3462871047
   ("" (skeep)
    (("" (skeep)
      (("" (lemma "between_point_is_wtd_av")
        (("" (inst - "x" "y" "w")
          (("" (assert)
( formula-declnilextra_real_propsnil)
              ((""    (posreal nonemp nilreal_typesnil)
                (""""!"java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
                  (" (assert)
                    (("" (replace -3 - rl)
                      (("" (inst)
                        ((""
                          ((" (skeepjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
                           "f(y) - t!1*f(y) = (1-t!1)*f(y)")
                          (( (" )
                          nil))
                        nil)
                      nil))
                    nil
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil
      nil))
    nil)
   ((  nil )
    (boolean nonempty-type-decl nil booleans                             -1f() =(-!)f())
     const-decl"[ >boolean] (1()n )("()nil)
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl niljava.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (convex? const-decl "bool" convex_functions nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (between_point_is_wtd_av formula-decl nil convex_functions nil))
   shostak))
 (loc_convex_min_is_connected 0
  (loc_convex_min_is_connected-1 nil 3462873854
   ("" (skeep)
    (("" (skeep)
      (("" (lemma "between_point_is_wtd_av")
        (("" (inst - "x" "y" "w")
          (("" (assert)
            (("" (skosimp*)
("( )
                (("" (  (loc_convex_min_is_connected-1 nil 3462873854
                  (("" (assert)
                    (("" (replace -3 - rl)(" replace- -"x""""w)
                      (("" (inst(( (  java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
                      nil))
                    ))
                  ))
l)java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   )java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> nil)java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
     nil
(number_fieldnonempty-type-from-decl  nil
    ( const-decl[ - ] java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 69
    (real nonempty-type-from-decl nil reals nil)
    (minus_odd_is_odd application-judgement "odd_int (real nonempty-type-from-decl nil )
    (convex? const-decl "bool" convex_functions nilconvexconst-decl"convex_functions)
    (real_plus_real_is_real application-judgement "real" reals nil)
    ( name-judgement?[real
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
      nilconvex_functionsnil
    (real_minus_real_is_real application-judgement "real" reals nil)
ecl convex_functionsnil)
stak
 (convex_btw_pt_left_lt 0
 620
   ("" (skeep)
    (("" (label "convexf" -1)
      (("(boolean nil java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 49
                    ("" (
          (("" (label "fac" -4)
            (("" (label "fbc" -5)
              (("" (label "fxc" 1)
                (("" (lemma "between_point_is_wtd_av2")
                  (("" (label "bpwa" -1)
                    (("" (inst((" expand "convex")
                      ( ()
                        (("" (skosimp*)
                          (("" (expand "convex?")
                            (("" (inst                                ("
                              ((""
                                (assert
                                ((""
                                  (copy "fac")
                                  ((""
                                    (mult-by -1 "1-t!1")
                                    ((""
nil)
                                      ((""
                                        (mult-by -1 "t!1")
nil
                                          (add-formulas -1 -2)
                                          nil
                                          
                                        nil))
                                      nil(between_point_is_wtd_av2formula-declnilconvex_functionsnil
                                    nil))
                                  nil))
                                
                              nil)    (( const-decl"numfield,numfield >numfield" java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
                            nil))
                          nil))
    (both_sides_times_pos_lt1 formula-decl nil real_props    (= const-decl "[T, T -> boolean]" equalities    (real_ge_is_total_order name-judgement " (convex? const-decl "bool" convex_functions nil)
                      nil    (numfield nonempty-type-eq-decl nil number_fields      "(strict_total_order?[real])" real_props nil)
                    nil))
                      (both_sides_times_pos_le1_imp formula-decl nil extra_real_props
                nil))
                 shostak))
                (real_le_is_total_order name-judgement  (loc_convex_min_is_connected-1 nil 3462873854
          nil))
        nil))
      nil))
    nil)
   ((between_point_is_wtd_av2 formula-decl nil convex_functions (convex_btw_pt_right_lt 0
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[ (("      (("" (label "Ax" -2)
     nil)
    (number_field nonempty-type-from-decl            (("" (label "fbc" -5)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real                  (("" (label "bpwa" -1)
    (< const-decl "bool" reals                       (("" (assert)
    (+ const-decl "[numfield, numfield -> ("  "w ("()nilnil nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (both_sides_times_pos_le1_imp formula-decl nil extra_real_props
     nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   shostak))
 (convex_btw_pt_right_lt 0
  (convex_btw_pt_right_lt-1 nil 3465122644
   ("" (skeep)
    (("" (label "convexf" -1)
      (("" (label "Ax" -2)
        (("" (label "Bx" -3)
          (("" (label "fac" -4)
            (("" (label "fbc" -5)
              (("" (label "fxc" 1)
                (("" (lemma "between_point_is_wtd_av2")
                  (("" (label "bpwa" -1)
                    (("" (inst - "A" "B" "x")
                      (("" (assert)
                        (("" (skosimp*)
(expandjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
                            (("" (inst - "Bjava.lang.StringIndexOutOfBoundsException: Range [43, 44) out of bounds for length 9
   "java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
                                (assert)
                                ((""
copy"java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 46
                                  ((""
                                    (mult-by -1 "1-t!1")
                                    ((java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
                                      (""( "bpwa real_propsniljava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
    (numfield nonempty-type-eq-decl nil number_fields nil)
                                        (mult-by -1 "t!1")
                  (""    (nonneg_real nonempty-type-eq-decl nil real_types nil)
                                          (add-formulas     (bool nonempty-type-eq-decl nil booleans nil)
                                          nil
                                          nil)    (real_le_is_total_order name-judgement "(total_order?[real])"
                                        nil))
                                      nil))
                                    nil))
                                  ))
                                nil))
                              nil))
                            nil))
                          nil)            (("" (mult-by -2 "t")
                        nil)                ((                                      "
                      nil))
                    nil      nil))
                  nil))
                nil)
              nil    number_field_predconst-decl"[ -boolean]"number_fields
                (number_field nonempty-type-from-decl nil number_fields nil)
          nil))
        nil))
      nil))
    nil)
    (  nilreal_typesnil)
    (number nonempty-type-decl    (number nonempty-type-decl ecl nil real_types nil)
    (boolean nonempty-type-decl nil      nil
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (<const-decl "ool reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (both_sides_times_pos_le1_imp formula-decl nil extra_real_props
     nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (>= const-decl "bool" reals nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil))
   nil))
 (convex_wtd_av_lt 0
  (convex_wtd_av_lt-1 nil 3466357784
   ("" (skeep)
    (("" (skeep)
      (("" (expand "convex?")
        (("" (inst - "x" "y" "t")
          (("" (assert)
            (("" (mult-by -2 "t")
              (("" (mult-by -3 "1-t")
                (("" (add-formulas -2 -3) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (>= const-decl "bool" reals nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (< const-decl "bool" reals nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (convex? const-decl "bool" convex_functions nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (real_tbsp;   (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)
    (real_plus_real_is_real application-judgement "real" reals nil))
   shostak))
 (convex_decreasing 0
  (convex_decreasing-1 nil 3487678783
   ("" (skeep)
    (("" (lemma "convex_btw_pt_left_lt")
      (("" (inst - "w" "x" "(f(v)-f(w))/2 + f(w)" "f" "v")
        (("" (assert) (("" (inst - "w") (("" (assert) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((convex_btw_pt_left_lt formula-decl nil convex_functions nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields 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)
    (real_plus_real_is_real application-judgement "real" reals nil))
   shostak))
 (strictly_convex_implies_convex 0
  (strictly_convex_implies_convex-1 nil 3466438530
   ("" (skeep)
    (("" (expand "strictly_convex?")
      (("" (expand "convex?")
        (("" (skeep)
          (("" (case "t = 0")
            (("1" (replace -1) (("1" (assert) nil nil)) nil)
             ("2" (case "t = 1")
              (("1" (replace -1) (("1" (assert) nil nil)) nil)
               ("2" (inst - "x" "y" "t") (("2" (assert) nil nil)) nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (convex? const-decl "bool" convex_functions nil))
   shostak))
 (strictly_convex_unique_min 0
  (strictly_convex_unique_min-1 nil 3462701259
   ("" (skosimp*)
java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 36
      (    (real_ge_is_total_order name-judgement "(total_order?[real])"     nil)
        (("" (assert)
          (("" (inst - "1 / 2 * x!1 (posreal nonempty-type-eq-decl (real_plus_real_is_real application-judgement "real" reals nil))
            ( (convex_decreasing 0
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real]) nil))
    (real_lt_is_strict_total_order name-judgement
     real_props nil    (("" (skeep)
    (        (("" (inst - "x" "y" "t")
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
        (nznum nonempty-type-eq-decl nil number_fields nil)
    (/ const-decl "[numfield, nznum -> numfield]" number_fields nil)
    (nznum nonempty-type-eq-decl nil number_fields nil)
    (/= const-decl "boolean" notequal nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil))
   shostak))
 (strictly_conv_uniq_intv_min 0
  (strictly_conv_uniq_intv_min-1 nil 3462701814
   ("" (skosimp*)
    (("" (expand            (nonneg_real nonempty-type-eq-decl nil real_types nil)
      ((""  (("1" (replace -1) (("1" (assert) nil nil)) nil)
        (("" (inst - "x!1" "y!1" "1/2")
          ((" real_props nil)
            (("" (inst - "1 / 2 * x!1 - 1 / 2 * y!1 + y!1")
                  (< const-decl "bool" reals             nil))
                nil))
    (- const-decl "[numfield, numfield
            nil))
          nil))
        nil))
      nil     "(strict_total_order?[real])" real_props nil)
    nil)
   ((real_times_real_is_real     "(strict_total_order?[real])" real_props nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (real_lt_is_strict_total_order
     "(strict_total_order?[real])" real_props nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_minus_real_is_real application-judgement "real (("" (split)
    (    (real_pred const-decl "[number_field -> boolean]" reals nil)
        (real nonempty-type-from-decl nil reals nil)
            nil   (
     java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 8
    (nznum nonempty-type-eq-decl nil number_fields    (real_lt_is_strict_total_order name-judgement
                ((""  ))
     real_props 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 " (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
     nil)
    booleannonempty-type-decl nilbooleansnil
    (number nonempty-type-decl nil numbers nil)
    (posrat_div_posrat_is_posrat application-judgement "posrat"
     rationals nil))
   ))
 (? const-decl "bool" convex_functions nil
  (composition_of_strictly_convex-1 nil 34    (real_lt_is_strict_total_order
   " skeep)
    (("" (expand "strictly_convex?")
      (("" (expand "convex?")
        (("" (skeep)
          (("" (expand "o nil))
            (("" (inst -2 "x" "y" "t")
              ( const-decl [,numfield    convex_btw_pt_left_ltformula-declnil convex_functionsnil
                (
                  (inst-"f( * (real_lt_is_strict_total_order name-judgement
                   "f(y) - t * f(y) + t * f(x)")
                  (("" (assert)
                    (("" (inst - "f(x)" "f(y)" "t")
                      (("" (assert) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
        (number_field nonempty-type-from-decl nil number_fields nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_minus_real_is_real application-judgement "real" reals nil)
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (O const-decl "T3" function_props nil)
    (convex? const-decl "bool" convex_functions nil))
   nil))
 (max_of_strictly_convex 0
  (max_of_strictly_convex-1 nil 3462703577
   ("" (skeep)
    (("" (expand "strictly_convex?")
      (("" (skeep)
        (("" (inst?)
          (("" (inst?)
            (("" (assert)
              (("" (hide -3)
                (("" (hide -3)
                  ((""
                    (case "f(t * x - t * y + y) >= g(t * x - t * y + y) or f(t * x - t * y + y) < g(t * x - t * y + y)")
                    (("1" (case "f(y) >= g(y) or f(y) < g(y)")
                      (("1" (case "f(x) >= g(x) or f(x) < g(x)")
                        (("1" (prop)
                          (("1" (expand "max") (("1" (assert) nil nil))
                            nil)
                           ("2" (expand "max")
                            (("2" (assert)
                              (("2"
                                (mult-by -2 "(1-t)")
                                (("2"
                                  (mult-by -3 "t")
                                  (("2" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("3" (expand "max")
                            (("3" (assert)
                              (("3"
                                (mult-by -2 "(1-t)")
                                (("3"
                                  (mult-by -3 "t")
                                  (("3" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("4" (expand "max")
                            (("4" (assert)
                              (("4"
                                (mult-by -2 "(1-t)")
                                (("4"
                                  (mult-by -3 "t")
                                  (("4" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("5" (expand "max")
                            (("5" (assert)
                              (("5"
                                (mult-by -2 "(1-t)")
                                (("5"
                                  (mult-by -3 "t")
                                  (("5" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("6" (expand "max")
                            (("6" (assert)
                              (("6"
                                (mult-by -2 "(1-t)")
                                (("6"
                                  (mult-by -3 "t")
                                  (("6" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("7" (expand "max")
                            (("7" (assert)
                              (("7"
                                (mult-by -2 "(1-t)")
                                (("7"
                                  (mult-by -3 "t")
                                  (("7" (assert) nil nil))
                                  nil))
                                nil))
                              nil))
                            nil)
                           ("8" (expand "max") (("8" (assert) nil nil))
                            nil))
                          nil)
                         ("2" (mult-by -3 "t")
                          (("2" (hide-all-but 1)
                            (("2" (grind) nil nil)) nil))
                          nil))
                        nil)
                       ("2" (hide-all-but 1) (("2" (grind) nil nil))
                        nil))
                      nil)
                     ("2" (hide-all-but 1) (("2" (grind) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
     nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
--> --------------------

--> maximum size reached

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

quality100%

br>                         nil)
                       ("2" (hide-all-but 1) (("2" (grind) nil nil))
                        nil))
                      nil)
                     ("2" (hide-all-but 1) (("2" (grind) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((real_times_real_is_real application-judgement "real" reals nil)
    (real_plus_real_is_real application-judgement "real" reals nil)
    (strictly_convex? const-decl "bool" convex_functions nil)
    (number nonempty-type-decl nil numbers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (nonneg_real nonempty-type-eq-decl nil real_types nil)
    (both_sides_times_pos_ge1_imp formula-decl nil extra_real_props
     nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (posreal nonempty-type-eq-decl nil real_types nil)
    (> const-decl "bool" reals nil)
    (both_sides_times_pos_lt1 formula-decl nil real_props nil)
    (bool nonempty-type-eq-decl nil booleans nil)
--> --------------------

--> maximum size reached

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

quality100%

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