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(card_lt_is_irreflexive 0
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("" (expand * "irreflexive?" "card_lt" )
(("" (skolem!)
(("" (inst + "identity[(x!1)]" ) (("" (judgement-tcc) nil nil ))
nil ))
nil ))
nil )
((injective? const-decl "bool" functions nil )
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(identity const-decl "(bijective?[T, T])" identity nil )
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(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(T formal-type-decl nil card_single nil )
(irreflexive? const-decl "bool" relations nil )
(card_lt const-decl "bool" card_comp_set nil ))
nil ))
(card_le_is_reflexive 0
(card_le_is_reflexive-1 nil 3316968557
("" (expand * "reflexive?" "card_le" )
(("" (skolem!)
(("" (inst + "identity[(x!1)]" ) (("" (judgement-tcc) nil nil ))
nil ))
nil ))
nil )
((injective? const-decl "bool" functions nil )
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(boolean nonempty-type-decl nil booleans nil )
(T formal-type-decl nil card_single nil )
(reflexive? const-decl "bool" relations nil )
(card_le const-decl "bool" card_comp_set nil ))
nil ))
(card_eq_is_reflexive 0
(card_eq_is_reflexive-1 nil 3316968557
("" (expand * "reflexive?" "card_eq" )
(("" (skolem!)
(("" (inst + "identity[(x!1)]" ) (("" (assert ) nil nil )) nil ))
nil ))
nil )
((identity const-decl "(bijective?[T, T])" identity nil )
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(boolean nonempty-type-decl nil booleans nil )
(T formal-type-decl nil card_single nil )
(reflexive? const-decl "bool" relations nil )
(card_eq const-decl "bool" card_comp_set nil ))
nil ))
(card_ge_is_reflexive 0
(card_ge_is_reflexive-1 nil 3316968557
("" (expand * "reflexive?" "card_ge" )
(("" (skolem!)
(("" (inst + "identity[(x!1)]" ) (("" (judgement-tcc) nil nil ))
nil ))
nil ))
nil )
((injective? const-decl "bool" functions nil )
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(boolean nonempty-type-decl nil booleans nil )
(T formal-type-decl nil card_single nil )
(reflexive? const-decl "bool" relations nil )
(card_ge const-decl "bool" card_comp_set nil ))
nil ))
(card_gt_is_irreflexive 0
(card_gt_is_irreflexive-1 nil 3316968557
("" (expand * "irreflexive?" "card_gt" )
(("" (skolem!)
(("" (inst + "identity[(x!1)]" ) (("" (judgement-tcc) nil nil ))
nil ))
nil ))
nil )
((injective? const-decl "bool" functions nil )
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(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(T formal-type-decl nil card_single nil )
(irreflexive? const-decl "bool" relations nil )
(card_gt const-decl "bool" card_comp_set nil ))
nil ))
(card_lt_is_antisymmetric 0
(card_lt_is_antisymmetric-1 nil 3316968557
("" (expand "antisymmetric?" )
(("" (skosimp)
(("" (forward-chain "card_lt_anticommutative" ) nil nil )) nil ))
nil )
((T formal-type-decl nil card_single nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(card_lt_anticommutative formula-decl nil card_comp_set_props nil )
(antisymmetric? const-decl "bool" relations nil ))
nil ))
(card_eq_is_symmetric 0
(card_eq_is_symmetric-1 nil 3316968557
("" (expand "symmetric?" )
(("" (skosimp) (("" (rewrite "card_eq_symmetric" ) nil nil )) nil ))
nil )
((T formal-type-decl nil card_single nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(card_eq_symmetric formula-decl nil card_comp_set_props nil )
(card_eq_is_reflexive name-judgement "(reflexive?[set[T]])"
card_single nil )
(symmetric? const-decl "bool" relations nil ))
nil ))
(card_gt_is_antisymmetric 0
(card_gt_is_antisymmetric-1 nil 3316968557
("" (expand "antisymmetric?" )
(("" (skosimp)
(("" (forward-chain "card_gt_anticommutative" ) nil nil )) nil ))
nil )
((T formal-type-decl nil card_single nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(card_gt_anticommutative formula-decl nil card_comp_set_props nil )
(antisymmetric? const-decl "bool" relations nil ))
nil ))
(card_lt_is_transitive 0
(card_lt_is_transitive-1 nil 3316968557
("" (expand "transitive?" )
(("" (skosimp) (("" (forward-chain "card_lt_transitive" ) nil nil ))
nil ))
nil )
((T formal-type-decl nil card_single nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(card_lt_transitive formula-decl nil card_comp_set_transitive nil )
(transitive? const-decl "bool" relations nil ))
nil ))
(card_le_is_transitive 0
(card_le_is_transitive-1 nil 3316968557
("" (expand "transitive?" )
(("" (skosimp) (("" (forward-chain "card_le_transitive" ) nil nil ))
nil ))
nil )
((T formal-type-decl nil card_single nil )
(set type-eq-decl nil sets nil )
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(boolean nonempty-type-decl nil booleans nil )
(card_le_transitive formula-decl nil card_comp_set_transitive nil )
(transitive? const-decl "bool" relations nil ))
nil ))
(card_eq_is_transitive 0
(card_eq_is_transitive-1 nil 3316968557
("" (expand "transitive?" )
(("" (skosimp) (("" (forward-chain "card_eq_transitive" ) nil nil ))
nil ))
nil )
((T formal-type-decl nil card_single nil )
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(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(card_eq_transitive formula-decl nil card_comp_set_transitive nil )
(transitive? const-decl "bool" relations nil ))
nil ))
(card_ge_is_transitive 0
(card_ge_is_transitive-1 nil 3316968557
("" (expand "transitive?" )
(("" (skosimp) (("" (forward-chain "card_ge_transitive" ) nil nil ))
nil ))
nil )
((T formal-type-decl nil card_single nil )
(set type-eq-decl nil sets nil )
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(boolean nonempty-type-decl nil booleans nil )
(card_ge_transitive formula-decl nil card_comp_set_transitive nil )
(transitive? const-decl "bool" relations nil ))
nil ))
(card_gt_is_transitive 0
(card_gt_is_transitive-1 nil 3316968557
("" (expand "transitive?" )
(("" (skosimp) (("" (forward-chain "card_gt_transitive" ) nil nil ))
nil ))
nil )
((T formal-type-decl nil card_single nil )
(set type-eq-decl nil sets nil )
(bool nonempty-type-eq-decl nil booleans nil )
(boolean nonempty-type-decl nil booleans nil )
(card_gt_transitive formula-decl nil card_comp_set_transitive nil )
(transitive? const-decl "bool" relations nil ))
nil ))
(card_le_is_dichotomous 0
(card_le_is_dichotomous-1 nil 3316968557
("" (expand "dichotomous?" )
(("" (skolem!) (("" (use "card_le_dichotomous" ) nil nil )) nil ))
nil )
((T formal-type-decl nil card_single nil )
(card_le_dichotomous formula-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 )
(dichotomous? const-decl "bool" orders nil ))
nil ))
(card_ge_is_dichotomous 0
(card_ge_is_dichotomous-1 nil 3316968557
("" (expand "dichotomous?" )
(("" (skolem!) (("" (use "card_ge_dichotomous" ) nil nil )) nil ))
nil )
((T formal-type-decl nil card_single nil )
(card_ge_dichotomous formula-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 )
(dichotomous? const-decl "bool" orders nil ))
nil ))
(card_eq_is_equivalence 0
(card_eq_is_equivalence-1 nil 3316968557 ("" (judgement-tcc) nil nil )
((card_eq_is_transitive name-judgement "(transitive?[set[T]])"
card_single nil )
(card_eq_is_symmetric name-judgement "(symmetric?[set[T]])"
card_single nil )
(card_eq_is_reflexive name-judgement "(reflexive?[set[T]])"
card_single nil )
(equivalence? const-decl "bool" relations nil ))
nil )))
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