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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: Extraction.v   Sprache: PVS

Original von: PVS©

(function_props_aux
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   ("" (skosimp)
    (("" (apply-extensionality :hide? t)
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        (("" (expand "o ")
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        nil))
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    nil)
   ((T1 formal-type-decl nil function_props_aux nil)
    (boolean nonempty-type-decl nil booleans nil)
    (O const-decl "T3" function_props nil)
    (T3 formal-type-decl nil function_props_aux nil)
    (inverse_image const-decl "set[D]" function_image nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (T2 formal-type-decl nil function_props_aux nil)
    (member const-decl "bool" sets nil))
   shostak))
 (composition_inverse_alt_TCC1 0
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   ("" (skosimp)
    (("" (typepred "f1!1")
      (("" (typepred "f2!1")
        (("" (expand "bijective?")
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            (("" (expand "surjective?")
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    (T1 formal-type-decl nil function_props_aux nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
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    (boolean nonempty-type-decl nil booleans nil)
    (surjective? const-decl "bool" functions nil)
    (T3 formal-type-decl nil function_props_aux nil))
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    (("" (typepred "f1!1")
      (("" (expand "bijective?")
        (("" (expand "surjective?")
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    (NOT const-decl "[bool -> bool]" booleans nil)
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    (boolean nonempty-type-decl nil booleans nil)
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   ((bijective? const-decl "bool" functions nil)
    (T3 formal-type-decl nil function_props_aux nil)
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    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (surjective? const-decl "bool" functions nil))
   shostak))
 (composition_inverse_alt 0
  (composition_inverse_alt-1 nil 3301540008
   ("" (skosimp)
    (("" (typepred "f1!1")
      (("" (typepred "f2!1")
        (("" (apply-extensionality :hide? t)
          (("1"
            (lemma "composition_bijective[T1,T2,T3]"
             ("f1" "f1!1" "f2" "f2!1"))
            (("1"
              (lemma "unique_bijective_inverse_alt[T1,T3]"
               ("f" "f2!1 o f1!1" "r" "x!1"))
              (("1"
                (lemma "unique_bijective_inverse_alt[T2,T3]"
                 ("f" "f2!1" "r" "x!1"))
                (("1"
                  (lemma "unique_bijective_inverse_alt[T1,T2]"
                   ("f" "f1!1" "r" "inverse_alt(f2!1)(x!1)"))
                  (("1" (expand "o" 1 2)
                    (("1" (expand "bijective?")
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                        (("1" (expand "injective?")
                          (("1"
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                               ("2"
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              (("2" (expand "surjective?")
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           ("3" (hide -1)
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                    (("4" (skosimp)
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    (T2 formal-type-decl nil function_props_aux nil)
    (T1 formal-type-decl nil function_props_aux nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (O const-decl "T3" function_props nil)
    (inverse_alt const-decl "inverses(f)" function_inverse_alt nil)
    (inverses nonempty-type-eq-decl nil function_inverse_alt nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (unique_bijective_inverse_alt application-judgement
     "{d | f(d) = r}" function_inverse_alt nil)
    (bijective_inverse_alt_is_bijective application-judgement
     "(bijective?[R, D])" function_inverse_alt nil)
    (composition_bijective application-judgement "(bijective?[T1, T3])"
     function_props nil)
    (composition_surjective application-judgement
     "(surjective?[T1, T3])" function_props nil)
    (composition_injective application-judgement "(injective?[T1, T3])"
     function_props nil)
    (unique_bijective_inverse_alt judgement-tcc nil
     function_inverse_alt nil)
    (injective? const-decl "bool" functions nil)
    (composition_bijective judgement-tcc nil function_props nil)
    (T3 formal-type-decl nil function_props_aux nil))
   shostak)))


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