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Datei: ring_with_one.prf Sprache: Lisp

Original von: PVS^©

(ring_with_one
(IMP_ring_TCC1 0
  (IMP_ring_TCC1-1 nil 3293390922
   ("" (lemma "fullset_is_ring_with_one")
    (("" (expand "ring_with_one?")
      (("" (flatten)
        (("" (expand "ring?") (("" (postpone) nil nil)) nil)) nil))
      nil))
    nil)
   ((ring_with_one? const-decl "bool" ring_with_one_def nil)
    (fullset_is_ring_with_one formula-decl nil ring_with_one nil))
   shostak))
(IMP_monoid_TCC1 0
  (IMP_monoid_TCC1-1 nil 3293390922
   ("" (lemma "fullset_is_ring_with_one")
    (("" (expand "ring_with_one?") (("" (flatten) nil nil)) nil)) nil)
   ((ring_with_one? const-decl "bool" ring_with_one_def nil)
    (fullset_is_ring_with_one formula-decl nil ring_with_one nil))
   shostak))
(ring_with_one_TCC1 0
  (ring_with_one_TCC1-1 nil 3293390922
   ("" (lemma "fullset_is_ring_with_one") (("" (propax) nil nil)) nil)
   ((fullset_is_ring_with_one formula-decl nil ring_with_one nil))
   shostak))
(one_times 0
  (one_times-1 nil 3293907997
   ("" (lemma "left_identity[T,*,one]") (("" (propax) nil nil)) nil)
   ((left_identity formula-decl nil monad nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (one formal-const-decl "T" ring_with_one nil))
   shostak))
(times_one 0
  (times_one-1 nil 3293908022
   ("" (lemma "right_identity[T,*,one]") (("" (propax) nil nil)) nil)
   ((right_identity formula-decl nil monad nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (one formal-const-decl "T" ring_with_one nil))
   shostak))
(unique_left_identity 0
  (unique_left_identity-1 nil 3293908031
   ("" (skosimp)
    ((""
      (lemma "unique_left_identity[T,*,one]"
       ("y" "y!1" "M" "fullset[T]"))
      (("1" (prop)
        (("1" (skosimp)
          (("1" (inst - "x!1") (("1" (grind) nil nil)) nil)) nil)
         ("2" (skosimp) (("2" (inst - "x!1") nil nil)) nil))
        nil)
       ("2" (hide 2)
        (("2" (lemma "fullset_is_ring_with_one")
          (("2" (expand "ring_with_one?")
            (("2" (expand "monoid?") (("2" (flatten) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((one formal-const-decl "T" ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (fullset const-decl "set" sets nil)
    (monad nonempty-type-eq-decl nil monad nil)
    (monad? const-decl "bool" monad_def nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (unique_left_identity formula-decl nil monad nil)
    (x!1 skolem-const-decl "T" ring_with_one nil)
    (fullset_is_ring_with_one formula-decl nil ring_with_one nil)
    (monoid? const-decl "bool" monoid_def nil)
    (ring_with_one? const-decl "bool" ring_with_one_def nil))
   shostak))
(unique_right_identity 0
  (unique_right_identity-1 nil 3293908156
   ("" (skosimp)
    ((""
      (lemma "unique_right_identity[T,*,one]"
       ("M" "fullset[T]" "y" "y!1"))
      (("1" (prop)
        (("1" (skosimp)
          (("1" (inst - "x!1") (("1" (grind) nil nil)) nil)) nil)
         ("2" (skosimp) (("2" (inst - "x!1") nil nil)) nil))
        nil)
       ("2" (lemma "fullset_is_ring_with_one")
        (("2" (expand "ring_with_one?")
          (("2" (flatten)
            (("2" (expand "monoid?") (("2" (flatten) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((one formal-const-decl "T" ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (fullset const-decl "set" sets nil)
    (monad nonempty-type-eq-decl nil monad nil)
    (monad? const-decl "bool" monad_def nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (unique_right_identity formula-decl nil monad nil)
    (x!1 skolem-const-decl "T" ring_with_one nil)
    (ring_with_one? const-decl "bool" ring_with_one_def nil)
    (monoid? const-decl "bool" monoid_def nil)
    (fullset_is_ring_with_one formula-decl nil ring_with_one nil))
   shostak))
(minus_one_times 0
  (minus_one_times-1 nil 3293956723
   ("" (skolem!)
    (("" (rewrite "negative_times")
      (("" (rewrite "one_times") nil nil)) nil))
    nil)
   ((left_identity formula-decl nil monad nil)
    (negative_times formula-decl nil ring nil)
    (one formal-const-decl "T" ring_with_one nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (+ formal-const-decl "[T, T -> T]" ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (zero formal-const-decl "T" ring_with_one nil))
   shostak))
(times_minus_one 0
  (times_minus_one-1 nil 3293956819
   ("" (skolem!)
    (("" (rewrite "times_negative")
      (("" (rewrite "times_one") nil nil)) nil))
    nil)
   ((right_identity formula-decl nil monad nil)
    (times_negative formula-decl nil ring nil)
    (one formal-const-decl "T" ring_with_one nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (+ formal-const-decl "[T, T -> T]" ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (zero formal-const-decl "T" ring_with_one nil))
   shostak))
(minus_one_sq_is_one 0
  (minus_one_sq_is_one-1 nil 3293956844
   ("" (assert)
    (("" (rewrite "minus_one_times")
      (("" (rewrite "negate_negate") nil nil)) nil))
    nil)
   ((inv_inv formula-decl nil group nil)
    (minus_one_times formula-decl nil ring_with_one nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (AND const-decl "[bool, bool -> bool]" booleans nil)
    (= const-decl "[T, T -> boolean]" equalities nil)
    (+ formal-const-decl "[T, T -> T]" ring_with_one nil)
    (zero formal-const-decl "T" ring_with_one nil)
    (inv const-decl "{y | x * y = one AND y * x = one}" group nil)
    (one formal-const-decl "T" ring_with_one nil))
   shostak))
(ring_with_one_is_ring 0
  (ring_with_one_is_ring-1 nil 3293390922
   ("" (skosimp)
    (("" (typepred "x!1")
      (("" (expand "ring_with_one?") (("" (flatten) nil nil)) nil))
      nil))
    nil)
   ((ring_with_one nonempty-type-eq-decl nil ring_with_one nil)
    (ring_with_one? const-decl "bool" ring_with_one_def nil)
    (one formal-const-decl "T" ring_with_one nil)
    (zero formal-const-decl "T" ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (+ formal-const-decl "[T, T -> T]" ring_with_one nil)
    (set type-eq-decl nil sets nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   shostak))
(ring_with_one_is_monoid 0
  (ring_with_one_is_monoid-1 nil 3293390922
   ("" (skosimp*)
    (("" (typepred "x!1")
      (("" (expand "ring_with_one?") (("" (flatten) nil nil)) nil))
      nil))
    nil)
   ((ring_with_one nonempty-type-eq-decl nil ring_with_one nil)
    (ring_with_one? const-decl "bool" ring_with_one_def nil)
    (one formal-const-decl "T" ring_with_one nil)
    (zero formal-const-decl "T" ring_with_one nil)
    (* formal-const-decl "[T, T -> T]" ring_with_one nil)
    (+ formal-const-decl "[T, T -> T]" ring_with_one nil)
    (set type-eq-decl nil sets nil)
    (T formal-nonempty-type-decl nil ring_with_one nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil))
   shostak)))

¤ Dauer der Verarbeitung: 0.19 Sekunden (vorverarbeitet) ¤

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