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Datei: relation_implication.prf Sprache: Lisp

Original von: PVS^©

(relation_implication
(rel_impl_extensionality 0
  (rel_impl_extensionality-1 nil 3570350716
   ("" (skosimp*)
    (("" (expand "|-") (("" (inst?) (("" (prop) nil nil)) nil)) nil))
    nil)
   ((\|- const-decl "bool" relation_implication nil)
    (U formal-nonempty-type-decl nil relation_implication nil)
    (T formal-nonempty-type-decl nil relation_implication nil))
   shostak))
(lemma_double_impl 0
  (lemma_double_impl-1 nil 3570774110
   ("" (skolem-typepred)
    (("" (flatten)
      (("" (expand "|=")
        (("" (prop)
          (("" (expand "|-")
            (("" (skolem!)
              (("" (inst?) (("" (inst?) (("" (prop) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((U formal-nonempty-type-decl nil relation_implication nil)
    (T formal-nonempty-type-decl nil relation_implication nil)
    (\|- const-decl "bool" relation_implication nil)
    (\|= const-decl "bool" relation_implication nil))
   shostak))
(rel_impl_is_partial_order 0
  (rel_impl_is_partial_order-1 nil 3570351379
   ("" (expand "partial_order?")
    (("" (prop)
      (("1" (expand "preorder?")
        (("1" (prop)
          (("1" (expand "reflexive?")
            (("1" (skolem-typepred)
              (("1" (expand "|-")
                (("1" (skolem!) (("1" (flatten) nil nil)) nil)) nil))
              nil))
            nil)
           ("2" (expand "transitive?")
            (("2" (skolem!)
              (("2" (flatten)
                (("2" (expand "|-")
                  (("2" (skolem!)
                    (("2" (inst?)
                      (("2" (inst?) (("2" (prop) nil nil)) nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "antisymmetric?")
        (("2" (skolem!)
          (("2" (flatten)
            (("2" (expand "|-")
              (("2" (apply-extensionality :hide? t)
                (("2" (inst?)
                  (("2" (inst?)
                    (("2" (iff) (("2" (prop) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((\|- const-decl "bool" relation_implication nil)
    (reflexive? const-decl "bool" relations nil)
    (U formal-nonempty-type-decl nil relation_implication nil)
    (T formal-nonempty-type-decl nil relation_implication nil)
    (transitive? const-decl "bool" relations nil)
    (preorder? const-decl "bool" orders nil)
    (pred type-eq-decl nil defined_types nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (antisymmetric? const-decl "bool" relations nil)
    (partial_order? const-decl "bool" orders nil))
   shostak))
(double_impl_is_equivalence 0
  (double_impl_is_equivalence-1 nil 3570774215
   ("" (expand "equivalence?")
    (("" (prop)
      (("1" (expand "reflexive?")
        (("1" (skolem!)
          (("1" (expand "|=")
            (("1" (prop)
              (("1" (expand "|-")
                (("1" (skolem!) (("1" (prop) nil nil)) nil)) nil)
               ("2" (expand "|-")
                (("2" (skolem!) (("2" (prop) nil nil)) nil)) nil))
              nil))
            nil))
          nil))
        nil)
       ("2" (expand "symmetric?")
        (("2" (skolem!)
          (("2" (prop) (("2" (expand "|=") (("2" (prop) nil nil)) nil))
            nil))
          nil))
        nil)
       ("3" (expand "transitive?")
        (("3" (skolem!)
          (("3" (flatten)
            (("3" (expand "|=")
              (("3" (expand "|-")
                (("3" (prop)
                  (("1" (skolem!)
                    (("1" (inst?)
                      (("1" (inst?)
                        (("1" (inst?)
                          (("1" (inst?) (("1" (prop) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil)
                   ("2" (skolem!)
                    (("2" (inst?)
                      (("2" (inst?)
                        (("2" (inst?)
                          (("2" (inst?) (("2" (prop) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((\|- const-decl "bool" relation_implication nil)
    (\|= const-decl "bool" relation_implication nil)
    (reflexive? const-decl "bool" relations nil)
    (symmetric? const-decl "bool" relations nil)
    (U formal-nonempty-type-decl nil relation_implication nil)
    (T formal-nonempty-type-decl nil relation_implication nil)
    (transitive? const-decl "bool" relations nil)
    (equivalence? const-decl "bool" relations nil))
   shostak))
(turnstile_TCC1 0
  (turnstile_TCC1-1 nil 3570774066
   ("" (judgement-tcc)
    (("" (apply-extensionality :hide? t)
      (("" (inst?)
        (("" (inst?) (("" (iff) (("" (prop) nil nil)) nil)) nil)) nil))
      nil))
    nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (pred type-eq-decl nil defined_types nil)
    (U formal-nonempty-type-decl nil relation_implication nil)
    (T formal-nonempty-type-decl nil relation_implication nil)
    (partial_order? const-decl "bool" orders nil)
    (antisymmetric? const-decl "bool" relations nil)
    (preorder? const-decl "bool" orders nil)
    (transitive? const-decl "bool" relations nil)
    (reflexive? const-decl "bool" relations nil)
    (\|- const-decl "bool" relation_implication nil))
   nil))
(models_TCC1 0
  (models_TCC1-1 nil 3570774066 ("" (judgement-tcc) nil nil)
   ((U formal-nonempty-type-decl nil relation_implication nil)
    (T formal-nonempty-type-decl nil relation_implication nil)
    (\|- const-decl "bool" relation_implication nil)
    (\|= const-decl "bool" relation_implication nil)
    (reflexive? const-decl "bool" relations nil)
    (symmetric? const-decl "bool" relations nil)
    (transitive? const-decl "bool" relations nil)
    (equivalence? const-decl "bool" relations nil))
   nil)))

¤ Dauer der Verarbeitung: 0.16 Sekunden (vorverarbeitet) ¤

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