Quelle continuous_lambda.prf Sprache: Lisp

(continuous_lambda
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(add_cont 0
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    (real_plus_real_is_real application-judgement "real" reals nil)
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   shostak))
(sub_cont 0
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      nil))
    nil)
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(neg_cont 0
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   shostak))
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    (real_times_real_is_real application-judgement "real" reals nil)
    (* const-decl "[T -> real]" real_fun_ops "reals/")
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   nil))
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   ("" (skeep)
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   nil))
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   shostak))
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   ("" (skeep)
    (("" (rewrite "div_cont") (("" (rewrite "const_cont") nil nil))
      nil))
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    (bool nonempty-type-eq-decl nil booleans nil)
    (continuous? const-decl "bool" continuous_functions nil)
    (continuous_fun nonempty-type-eq-decl nil continuous_functions nil)
    (/= const-decl "boolean" notequal nil)
    (nzreal nonempty-type-eq-decl nil reals nil)
    (nz_continuous_fun type-eq-decl nil continuous_functions nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
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   shostak))
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    nil)
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    (number_field_pred const-decl "[number -> boolean]" number_fields
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   shostak))
(pow_cont_TCC1 0
  (pow_cont_TCC1-1 nil 3443542015
   ("" (skosimp) (("" (assert) nil nil)) nil)
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     real_props nil))
   nil))
(pow_cont 0
  (pow_cont-1 nil 3443543278
   ("" (skeep)
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    nil)
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    (integer_pred const-decl "[rational -> boolean]" integers nil)
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   shostak))
(sq_cont 0
  (sq_cont-1 nil 3443541122
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(sqrt_cont_TCC1 0
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   ("" (skeep :preds? t)
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(sqrt_cont 0
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                  nil))
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              nil))
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            nil))
          nil))
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      nil))
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                  nil))
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        nil))
      nil))
    nil)
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     nil))
   shostak))
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   shostak))
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      (("1" (hide -1)
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          (("1" (rewrite "add_cont")
            (("1" (rewrite "add_cont")
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              nil))
            nil))
          nil))
        nil)
       ("2" (hide 2)
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           ("2" (hide 2)
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                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
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         nil)
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    (add_cont formula-decl nil continuous_lambda nil)
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    (f2 skolem-const-decl "continuous_fun[T]" continuous_lambda nil)
    (max_abs formula-decl nil min_max "reals/")
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil))
   shostak))
(min_cont 0
  (min_cont-1 nil 3443548048
   ("" (skolem 1 ("f1" "f2"))
    ((""
      (case-replace
       "(LAMBDA(x):min(f1(x),f2(x))) = (LAMBDA(x):-max(-f1(x),-f2(x)))")
      (("1" (hide -)
        (("1" (rewrite "neg_cont")
          (("1" (rewrite "max_cont")
            (("1" (rewrite "neg_cont") nil nil)
             ("2" (rewrite "neg_cont") nil nil))
            nil))
          nil))
        nil)
       ("2" (hide 2)
        (("2" (decompose-equality 1)
          (("1" (grind) nil nil)
           ("2" (skeep)
            (("2" (rewrite "min_max" :dir rl) (("2" (grind) nil nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((minus_real_is_real application-judgement "real" reals 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)
    (T_pred const-decl "[real -> boolean]" continuous_lambda nil)
    (T formal-subtype-decl nil continuous_lambda nil)
    (numfield nonempty-type-eq-decl nil number_fields nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (<= const-decl "bool" reals nil)
    (min const-decl "{p: real | p <= m AND p <= n}" real_defs nil)
    (continuous? const-decl "bool" continuous_functions nil)
    (continuous_fun nonempty-type-eq-decl nil continuous_functions nil)
    (- const-decl "[numfield -> numfield]" number_fields nil)
    (>= const-decl "bool" reals nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (neg_cont formula-decl nil continuous_lambda nil)
    (max_cont formula-decl nil continuous_lambda nil)
    (f1 skolem-const-decl "continuous_fun[T]" continuous_lambda nil)
    (f2 skolem-const-decl "continuous_fun[T]" continuous_lambda nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props 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)
    (min_max formula-decl nil min_max "reals/")
    (real_le_is_total_order name-judgement "(total_order?[real])"
     real_props nil))
   shostak)))

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Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

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