Quelle card_comp_set_props.prf Sprache: Lisp

(card_comp_set_props
(card_lt_surj 0
  (card_lt_surj-1 nil 3316959740
   ("" (skolem!)
    (("" (expand "card_lt")
      (("" (prop)
        (("1" (lemma "fun_exists[(S2!1), (S1!1)]")
          (("1" (prop)
            (("1" (skolem!)
              (("1" (inst 2 "f!1") (("1" (grind) nil nil)) nil)) nil))
            nil))
          nil)
         ("2" (skolem!)
          (("2" (use "surjective_inverse_exists[(S1!1), (S2!1)]")
            (("2" (skolem!)
              (("2" (use "inj_inv_alt[(S1!1), (S2!1)]")
                (("2" (inst?) nil nil)) nil))
              nil))
            nil))
          nil)
         ("3" (skolem! -2)
          (("3" (use "inv_inj_is_surj[(S2!1), (S1!1)]")
            (("3" (inst?) nil nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((card_lt const-decl "bool" card_comp_set nil)
    (inverse const-decl "D" function_inverse nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]" card_comp_set_props
     nil)
    (inv_inj_is_surj judgement-tcc nil function_inverse nil)
    (TRUE const-decl "bool" booleans nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (g!1 skolem-const-decl "[(S2!1) -> (S1!1)]" card_comp_set_props
     nil)
    (inj_inv_alt formula-decl nil function_inverse_def nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]" card_comp_set_props
     nil)
    (surjective? const-decl "bool" functions nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_props nil)
    (surjective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (fun_exists formula-decl nil function_image nil)
    (injective? const-decl "bool" functions nil)
    (NOT const-decl "[bool -> bool]" booleans nil))
   shostak))
(card_ge_surj 0
  (card_ge_surj-1 nil 3316959991
   ("" (skolem!)
    (("" (expand "card_ge")
      (("" (split)
        (("1" (flatten)
          (("1" (skolem!)
            (("1" (case "EXISTS (x: (S2!1)): TRUE")
              (("1" (use "inv_inj_is_surj[(S2!1), (S1!1)]")
                (("1" (inst? 2) nil nil)) nil)
               ("2" (split)
                (("1" (lemma "fun_exists[(S1!1), (S2!1)]")
                  (("1" (prop)
                    (("1" (skolem!)
                      (("1" (inst 3 "f!2") (("1" (grind) nil nil))
                        nil))
                      nil))
                    nil))
                  nil)
                 ("2" (skolem!) (("2" (inst + "t!1") nil nil)) nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (prop)
          (("1" (skolem!)
            (("1" (inst + "LAMBDA (x: (S2!1)): t!1")
              (("1" (grind) nil nil)) nil))
            nil)
           ("2" (skolem!)
            (("2" (use "surjective_inverse_exists[(S1!1), (S2!1)]")
              (("2" (skolem!)
                (("2" (use "inj_inv_alt[(S1!1), (S2!1)]")
                  (("2" (inst?) nil nil)) nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((card_ge const-decl "bool" card_comp_set nil)
    (surjective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]" card_comp_set_props
     nil)
    (inj_inv_alt formula-decl nil function_inverse_def nil)
    (g!1 skolem-const-decl "[(S2!1) -> (S1!1)]" card_comp_set_props
     nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (TRUE const-decl "bool" booleans nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (inverse const-decl "D" function_inverse nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]" card_comp_set_props
     nil)
    (injective? const-decl "bool" functions nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_props nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_props nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (inv_inj_is_surj judgement-tcc nil function_inverse nil)
    (fun_exists formula-decl nil function_image nil)
    (surjective? const-decl "bool" functions nil)
    (NOT const-decl "[bool -> bool]" booleans nil))
   shostak))
(card_lt_le 0
  (card_lt_le-1 nil 3316960095
   ("" (expand* "card_lt" "card_le")
    (("" (skosimp)
      (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
        (("" (prop) nil nil)) nil))
      nil))
    nil)
   ((injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (T1 formal-type-decl nil card_comp_set_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (card_lt const-decl "bool" card_comp_set nil)
    (card_le const-decl "bool" card_comp_set nil))
   shostak))
(card_gt_ge 0
  (card_gt_ge-1 nil 3316960131
   ("" (expand* "card_gt" "card_ge")
    (("" (skosimp)
      (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
        (("" (prop) nil nil)) nil))
      nil))
    nil)
   ((injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (T1 formal-type-decl nil card_comp_set_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (card_gt const-decl "bool" card_comp_set nil)
    (card_ge const-decl "bool" card_comp_set nil))
   shostak))
(card_lt_gt 0
  (card_lt_gt-1 nil 3316960154
   ("" (expand* "card_lt" "card_gt") nil nil)
   ((card_gt const-decl "bool" card_comp_set nil)
    (card_lt const-decl "bool" card_comp_set nil))
   shostak))
(card_le_ge 0
  (card_le_ge-1 nil 3316960172
   ("" (expand* "card_le" "card_ge") nil nil)
   ((card_ge const-decl "bool" card_comp_set nil)
    (card_le const-decl "bool" card_comp_set nil))
   shostak))
(card_gt_lt 0
  (card_gt_lt-1 nil 3316960178
   ("" (expand* "card_gt" "card_lt") nil nil)
   ((card_lt const-decl "bool" card_comp_set nil)
    (card_gt const-decl "bool" card_comp_set nil))
   shostak))
(card_ge_le 0
  (card_ge_le-1 nil 3316960186
   ("" (expand* "card_ge" "card_le") nil nil)
   ((card_le const-decl "bool" card_comp_set nil)
    (card_ge const-decl "bool" card_comp_set nil))
   shostak))
(card_lt_ge 0
  (card_lt_ge-1 nil 3316960193
   ("" (expand* "card_lt" "card_ge" "XOR") (("" (reduce) nil nil)) nil)
   ((card_lt const-decl "bool" card_comp_set nil)
    (XOR const-decl "bool" xor_def nil)
    (card_ge const-decl "bool" card_comp_set nil))
   shostak))
(card_le_gt 0
  (card_le_gt-1 nil 3316960243
   ("" (expand* "card_le" "card_gt" "XOR") (("" (reduce) nil nil)) nil)
   ((card_le const-decl "bool" card_comp_set nil)
    (XOR const-decl "bool" xor_def nil)
    (card_gt const-decl "bool" card_comp_set nil))
   shostak))
(card_eq_le_ge 0
  (card_eq_le_ge-1 nil 3316960256
   ("" (expand* "card_eq" "card_le" "card_ge")
    (("" (skolem!)
      (("" (prop)
        (("1" (expand "bijective?")
          (("1" (skosimp) (("1" (inst?) nil nil)) nil)) nil)
         ("2" (skolem!)
          (("2" (use "bijective_inverse_exists[(S1!1), (S2!1)]")
            (("2" (expand "exists1")
              (("2" (skosimp*)
                (("2" (use "bij_inv_is_bij_alt[(S1!1), (S2!1)]")
                  (("2" (expand "bijective?" -1)
                    (("2" (flatten) (("2" (inst?) nil nil)) nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("3" (forward-chain "inj_inj_bij[(S1!1), (S2!1)]") nil nil))
        nil))
      nil))
    nil)
   ((inj_inj_bij formula-decl nil set_antisymmetric "orders/")
    (exists1 const-decl "bool" exists1 nil)
    (bij_inv_is_bij_alt formula-decl nil function_inverse_def nil)
    (x!1 skolem-const-decl "[(S2!1) -> (S1!1)]" card_comp_set_props
     nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]" card_comp_set_props
     nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_props nil)
    (bijective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (bijective? const-decl "bool" functions nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (card_eq const-decl "bool" card_comp_set nil)
    (card_ge const-decl "bool" card_comp_set nil)
    (card_le const-decl "bool" card_comp_set nil))
   shostak))
(card_le_lt_eq 0
  (card_le_lt_eq-1 nil 3316960340
   ("" (expand* "card_le" "card_lt" "card_eq")
    (("" (skolem!)
      (("" (prop)
        (("1" (forward-chain "inj_inj_bij[(S1!1), (S2!1)]") nil nil)
         ("2" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
          (("2" (prop) nil nil)) nil)
         ("3" (expand "bijective?")
          (("3" (skosimp) (("3" (inst?) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((bijective? const-decl "bool" functions nil)
    (injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (inj_inj_bij formula-decl nil set_antisymmetric "orders/")
    (T1 formal-type-decl nil card_comp_set_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (card_le const-decl "bool" card_comp_set nil)
    (card_eq const-decl "bool" card_comp_set nil)
    (card_lt const-decl "bool" card_comp_set nil))
   shostak))
(card_ge_gt_eq 0
  (card_ge_gt_eq-1 nil 3316960405
   ("" (skolem!)
    (("" (use "card_eq_le_ge")
      (("" (expand* "card_eq" "card_le" "card_ge" "card_gt")
        (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
          (("" (ground) nil nil)) nil))
        nil))
      nil))
    nil)
   ((card_eq_le_ge formula-decl nil card_comp_set_props nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (card_eq const-decl "bool" card_comp_set nil)
    (card_ge const-decl "bool" card_comp_set nil)
    (card_gt const-decl "bool" card_comp_set nil)
    (card_le const-decl "bool" card_comp_set nil))
   shostak))
(card_lt_neq_ngt 0
  (card_lt_neq_ngt-1 nil 3316960435
   ("" (skosimp)
    (("" (use "card_ge_gt_eq")
      (("" (use "card_lt_ge")
        (("" (expand "XOR") (("" (ground) nil nil)) nil)) nil))
      nil))
    nil)
   ((card_ge_gt_eq formula-decl nil card_comp_set_props nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (XOR const-decl "bool" xor_def nil)
    (card_lt_ge formula-decl nil card_comp_set_props nil))
   shostak))
(card_gt_neq_nlt 0
  (card_gt_neq_nlt-1 nil 3316960535
   ("" (expand* "card_gt" "card_eq" "card_lt")
    (("" (skosimp)
      (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
        (("" (prop)
          (("" (expand "bijective?")
            (("" (skosimp) (("" (inst?) nil nil)) nil)) nil))
          nil))
        nil))
      nil))
    nil)
   ((bijective? const-decl "bool" functions nil)
    (injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (T1 formal-type-decl nil card_comp_set_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (card_gt const-decl "bool" card_comp_set nil)
    (card_lt const-decl "bool" card_comp_set nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_lt_anticommutative 0
  (card_lt_anticommutative-1 nil 3316960578
   ("" (expand "card_lt")
    (("" (skosimp)
      (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
        (("" (prop) nil nil)) nil))
      nil))
    nil)
   ((injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (T1 formal-type-decl nil card_comp_set_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (card_lt const-decl "bool" card_comp_set nil))
   shostak))
(card_le_antisymmetric 0
  (card_le_antisymmetric-1 nil 3316960590
   ("" (expand* "card_le" "card_eq")
    (("" (skosimp)
      (("" (forward-chain "inj_inj_bij[(S1!1), (S2!1)]") nil nil))
      nil))
    nil)
   ((T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (inj_inj_bij formula-decl nil set_antisymmetric "orders/")
    (card_le const-decl "bool" card_comp_set nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_eq_symmetric 0
  (card_eq_symmetric-1 nil 3316960616
   ("" (expand "card_eq")
    (("" (skolem!)
      (("" (iff)
        (("" (prop)
          (("1" (skolem!)
            (("1" (use "bijective_inverse_exists[(S1!1), (S2!1)]")
              (("1" (expand "exists1")
                (("1" (skosimp*)
                  (("1" (use "bij_inv_is_bij_alt[(S1!1), (S2!1)]")
                    (("1" (inst?) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (skolem!)
            (("2" (use "bijective_inverse_exists[(S2!1), (S1!1)]")
              (("2" (expand "exists1")
                (("2" (skosimp*)
                  (("2" (use "bij_inv_is_bij_alt[(S2!1), (S1!1)]")
                    (("2" (inst?) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((bijective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_props nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_props nil)
    (bijective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]" card_comp_set_props
     nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (x!1 skolem-const-decl "[(S2!1) -> (S1!1)]" card_comp_set_props
     nil)
    (bij_inv_is_bij_alt formula-decl nil function_inverse_def nil)
    (exists1 const-decl "bool" exists1 nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]" card_comp_set_props
     nil)
    (x!1 skolem-const-decl "[(S1!1) -> (S2!1)]" card_comp_set_props
     nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_ge_antisymmetric 0
  (card_ge_antisymmetric-1 nil 3316960683
   ("" (expand* "card_ge" "card_eq")
    (("" (skosimp)
      (("" (forward-chain "inj_inj_bij[(S1!1), (S2!1)]") nil nil))
      nil))
    nil)
   ((T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (inj_inj_bij formula-decl nil set_antisymmetric "orders/")
    (card_ge const-decl "bool" card_comp_set nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_gt_anticommutative 0
  (card_gt_anticommutative-1 nil 3316960742
   ("" (expand "card_gt")
    (("" (skosimp)
      (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
        (("" (prop) nil nil)) nil))
      nil))
    nil)
   ((injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (T1 formal-type-decl nil card_comp_set_props nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (set type-eq-decl nil sets nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (card_gt const-decl "bool" card_comp_set nil))
   shostak))
(card_lt_trichotomous 0
  (card_lt_trichotomous-1 nil 3316960758
   ("" (skosimp)
    (("" (use "card_lt_ge")
      (("" (use "card_gt_lt")
        (("" (use "card_ge_gt_eq")
          (("" (expand "XOR") (("" (ground) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((card_lt_ge formula-decl nil card_comp_set_props nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (card_ge_gt_eq formula-decl nil card_comp_set_props nil)
    (XOR const-decl "bool" xor_def nil)
    (card_gt_lt formula-decl nil card_comp_set_props nil))
   shostak))
(card_le_dichotomous 0
  (card_le_dichotomous-1 nil 3316960784
   ("" (skosimp)
    (("" (use "card_le_gt")
      (("" (use "card_ge_le")
        (("" (use "card_gt_ge")
          (("" (expand "XOR") (("" (ground) nil nil)) nil)) nil))
        nil))
      nil))
    nil)
   ((card_le_gt formula-decl nil card_comp_set_props nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (card_gt_ge formula-decl nil card_comp_set_props nil)
    (XOR const-decl "bool" xor_def nil)
    (card_ge_le formula-decl nil card_comp_set_props nil))
   shostak))
(card_ge_dichotomous 0
  (card_ge_dichotomous-1 nil 3316960815
   ("" (skosimp)
    (("" (use "card_le_dichotomous")
      (("" (use "card_le_ge")
        (("" (use "card_ge_le") (("" (ground) nil nil)) nil)) nil))
      nil))
    nil)
   ((card_le_dichotomous formula-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (card_ge_le formula-decl nil card_comp_set_props nil)
    (card_le_ge formula-decl nil card_comp_set_props nil))
   shostak))
(card_gt_trichotomous 0
  (card_gt_trichotomous-1 nil 3316960841
   ("" (skosimp)
    (("" (use "card_lt_trichotomous")
      (("" (use "card_lt_gt")
        (("" (use "card_gt_lt") (("" (ground) nil nil)) nil)) nil))
      nil))
    nil)
   ((card_lt_trichotomous formula-decl nil card_comp_set_props nil)
    (T2 formal-type-decl nil card_comp_set_props nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T1 formal-type-decl nil card_comp_set_props nil)
    (card_gt_lt formula-decl nil card_comp_set_props nil)
    (card_lt_gt formula-decl nil card_comp_set_props nil))
   shostak)))

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