Quelle card_comp_set_transitive.prf Sprache: Lisp

(card_comp_set_transitive
(card_lt_transitive 0
  (card_lt_transitive-1 nil 3316966275
   ("" (expand "card_lt")
    (("" (skosimp)
      (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
        (("" (prop)
          (("" (skosimp*)
            (("" (use "composition_injective[(S3!1), (S1!1), (S2!1)]")
              (("" (inst? 2) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((composition_injective judgement-tcc nil function_props nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!2 skolem-const-decl "[(S3!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (O const-decl "T3" function_props nil)
    (injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (T1 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (card_lt const-decl "bool" card_comp_set nil))
   shostak))
(card_lt_le_transitive 0
  (card_lt_le_transitive-1 nil 3316966326
   ("" (expand* "card_lt" "card_le")
    (("" (skosimp*)
      (("" (use "composition_injective[(S2!1), (S3!1), (S1!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S3!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (T1 formal-type-decl nil card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_lt const-decl "bool" card_comp_set nil)
    (card_le const-decl "bool" card_comp_set nil))
   shostak))
(card_lt_eq_transitive 0
  (card_lt_eq_transitive-1 nil 3316966361
   ("" (expand* "card_lt" "card_eq" "bijective?")
    (("" (skosimp*)
      (("" (use "composition_injective[(S2!1), (S3!1), (S1!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S3!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (T1 formal-type-decl nil card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_lt const-decl "bool" card_comp_set nil)
    (bijective? const-decl "bool" functions nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_le_lt_transitive 0
  (card_le_lt_transitive-1 nil 3316966385
   ("" (expand* "card_le" "card_lt")
    (("" (skosimp*)
      (("" (use "composition_injective[(S3!1), (S1!1), (S2!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S3!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive nil)
    (T1 formal-type-decl nil card_comp_set_transitive nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_le const-decl "bool" card_comp_set nil)
    (card_lt const-decl "bool" card_comp_set nil))
   shostak))
(card_eq_lt_transitive 0
  (card_eq_lt_transitive-1 nil 3316966409
   ("" (expand* "card_eq" "card_lt" "bijective?")
    (("" (skosimp*)
      (("" (use "composition_injective[(S3!1), (S1!1), (S2!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!2 skolem-const-decl "[(S3!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive nil)
    (T1 formal-type-decl nil card_comp_set_transitive nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_eq const-decl "bool" card_comp_set nil)
    (bijective? const-decl "bool" functions nil)
    (card_lt const-decl "bool" card_comp_set nil))
   shostak))
(card_le_transitive 0
  (card_le_transitive-1 nil 3316966440
   ("" (expand "card_le")
    (("" (skosimp*)
      (("" (use "composition_injective[(S1!1), (S2!1), (S3!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_le const-decl "bool" card_comp_set nil))
   shostak))
(card_le_eq_transitive 0
  (card_le_eq_transitive-1 nil 3316966458
   ("" (expand* "card_le" "card_eq" "bijective?")
    (("" (skosimp*)
      (("" (use "composition_injective[(S1!1), (S2!1), (S3!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_le const-decl "bool" card_comp_set nil)
    (bijective? const-decl "bool" functions nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_eq_le_transitive 0
  (card_eq_le_transitive-1 nil 3316966499
   ("" (expand* "card_eq" "card_le" "bijective?")
    (("" (skosimp*)
      (("" (use "composition_injective[(S1!1), (S2!1), (S3!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_eq const-decl "bool" card_comp_set nil)
    (bijective? const-decl "bool" functions nil)
    (card_le const-decl "bool" card_comp_set nil))
   shostak))
(card_eq_transitive 0
  (card_eq_transitive-1 nil 3316966568
   ("" (expand "card_eq")
    (("" (skosimp*)
      (("" (use "composition_bijective[(S1!1), (S2!1), (S3!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (bijective? const-decl "bool" functions nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_bijective judgement-tcc nil function_props nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_eq_ge_transitive 0
  (card_eq_ge_transitive-1 nil 3316966605
   ("" (expand* "card_eq" "card_ge")
    (("" (skosimp*)
      (("" (use "bijective_inverse_exists[(S1!1), (S2!1)]")
        (("" (expand "exists1")
          (("" (skosimp*)
            (("" (use "bij_inv_is_bij_alt[(S1!1), (S2!1)]")
              (("" (expand "bijective?" -1)
                (("" (flatten)
                  ((""
                    (use "composition_injective[(S3!1), (S2!1), (S1!1)]")
                    (("" (inst?) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((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_transitive nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (O const-decl "T3" function_props nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!2 skolem-const-decl "[(S3!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (bijective? const-decl "bool" functions nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (bijective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (card_eq const-decl "bool" card_comp_set nil)
    (card_ge const-decl "bool" card_comp_set nil))
   shostak))
(card_ge_eq_transitive 0
  (card_ge_eq_transitive-1 nil 3316966787
   ("" (expand* "card_ge" "card_eq")
    (("" (skosimp*)
      (("" (use "bijective_inverse_exists[(S2!1), (S3!1)]")
        (("" (expand "exists1")
          (("" (skosimp*)
            (("" (use "bij_inv_is_bij_alt[(S2!1), (S3!1)]")
              (("" (expand "bijective?" -1)
                (("" (flatten)
                  ((""
                    (use "composition_injective[(S3!1), (S2!1), (S1!1)]")
                    (("" (inst?) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((exists1 const-decl "bool" exists1 nil)
    (bij_inv_is_bij_alt formula-decl nil function_inverse_def nil)
    (x!1 skolem-const-decl "[(S3!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (O const-decl "T3" function_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (composition_injective judgement-tcc nil function_props nil)
    (T1 formal-type-decl nil card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (bijective? const-decl "bool" functions nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (bijective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (card_ge const-decl "bool" card_comp_set nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_ge_transitive 0
  (card_ge_transitive-1 nil 3316966978
   ("" (expand "card_ge")
    (("" (skosimp*)
      (("" (use "composition_injective[(S3!1), (S2!1), (S1!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S3!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (T1 formal-type-decl nil card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive nil)
    (set type-eq-decl nil sets nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (boolean nonempty-type-decl nil booleans nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_ge const-decl "bool" card_comp_set nil))
   shostak))
(card_eq_gt_transitive 0
  (card_eq_gt_transitive-1 nil 3316967003
   ("" (expand* "card_eq" "card_gt")
    (("" (skosimp*)
      (("" (use "bijective_inverse_exists[(S1!1), (S2!1)]")
        (("" (expand "exists1")
          (("" (skosimp*)
            (("" (use "bij_inv_is_bij_alt[(S1!1), (S2!1)]")
              (("" (expand "bijective?" -1)
                (("" (flatten)
                  ((""
                    (use "composition_injective[(S2!1), (S1!1), (S3!1)]")
                    (("" (inst?) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((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_transitive nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (O const-decl "T3" function_props nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S1!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (composition_injective judgement-tcc nil function_props nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S1!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (bijective? const-decl "bool" functions nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (bijective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (card_eq const-decl "bool" card_comp_set nil)
    (card_gt const-decl "bool" card_comp_set nil))
   shostak))
(card_ge_gt_transitive 0
  (card_ge_gt_transitive-1 nil 3316967051
   ("" (expand* "card_ge" "card_gt")
    (("" (skosimp*)
      (("" (use "composition_injective[(S2!1), (S1!1), (S3!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S1!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (T1 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_ge const-decl "bool" card_comp_set nil)
    (card_gt const-decl "bool" card_comp_set nil))
   shostak))
(card_gt_eq_transitive 0
  (card_gt_eq_transitive-1 nil 3316967073
   ("" (expand* "card_gt" "card_eq")
    (("" (skosimp*)
      (("" (use "bijective_inverse_exists[(S2!1), (S3!1)]")
        (("" (expand "exists1")
          (("" (skosimp*)
            (("" (use "bij_inv_is_bij_alt[(S2!1), (S3!1)]")
              (("" (expand "bijective?" -1)
                (("" (flatten)
                  ((""
                    (use "composition_injective[(S1!1), (S3!1), (S2!1)]")
                    (("" (inst?) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((exists1 const-decl "bool" exists1 nil)
    (bij_inv_is_bij_alt formula-decl nil function_inverse_def nil)
    (x!1 skolem-const-decl "[(S3!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (inverse? const-decl "bool" function_inverse_def nil)
    (O const-decl "T3" function_props nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!2 skolem-const-decl "[(S1!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (T1 formal-type-decl nil card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (bijective? const-decl "bool" functions nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (bijective_inverse_exists formula-decl nil function_inverse_def
     nil)
    (card_gt const-decl "bool" card_comp_set nil)
    (card_eq const-decl "bool" card_comp_set nil))
   shostak))
(card_gt_ge_transitive 0
  (card_gt_ge_transitive-1 nil 3316967127
   ("" (expand* "card_gt" "card_ge")
    (("" (skosimp*)
      (("" (use "composition_injective[(S1!1), (S3!1), (S2!1)]")
        (("" (inst?) nil nil)) nil))
      nil))
    nil)
   ((O const-decl "T3" function_props nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (f!1 skolem-const-decl "[(S3!1) -> (S2!1)]"
     card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S1!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (T2 formal-type-decl nil card_comp_set_transitive nil)
    (T3 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (composition_injective judgement-tcc nil function_props nil)
    (card_gt const-decl "bool" card_comp_set nil)
    (card_ge const-decl "bool" card_comp_set nil))
   shostak))
(card_gt_transitive 0
  (card_gt_transitive-1 nil 3316967160
   ("" (expand "card_gt")
    (("" (skosimp)
      (("" (lemma "injective_dichotomous[(S1!1), (S2!1)]")
        (("" (prop)
          (("" (skosimp*)
            (("" (use "composition_injective[(S2!1), (S1!1), (S3!1)]")
              (("" (inst?) nil nil)) nil))
            nil))
          nil))
        nil))
      nil))
    nil)
   ((composition_injective judgement-tcc nil function_props nil)
    (T3 formal-type-decl nil card_comp_set_transitive nil)
    (S2!1 skolem-const-decl "set[T2]" card_comp_set_transitive nil)
    (S1!1 skolem-const-decl "set[T1]" card_comp_set_transitive nil)
    (injective? const-decl "bool" functions nil)
    (f!1 skolem-const-decl "[(S2!1) -> (S1!1)]"
     card_comp_set_transitive nil)
    (f!2 skolem-const-decl "[(S1!1) -> (S3!1)]"
     card_comp_set_transitive nil)
    (S3!1 skolem-const-decl "set[T3]" card_comp_set_transitive nil)
    (O const-decl "T3" function_props nil)
    (injective_dichotomous formula-decl nil set_dichotomous "orders/")
    (T1 formal-type-decl nil card_comp_set_transitive 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_transitive nil)
    (card_gt const-decl "bool" card_comp_set nil))
   shostak)))

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