Quelle symmetric_groups.prf
Sprache: Lisp
(symmetric_groupsnil 3251123754 ("" (grind) nil nil )"(bijective?[T1, T3])" nil )"(surjective?[T1, T3])" function_props nil )"(injective?[T1, T3])" nil ))nil ))nil 3407237323"" (expand "group?" )"" (prop)"1" (expand "monoid?" )"1" (prop)"1" (expand "monad?" )"1" (prop)"1" (expand "groupoid?" )"1" (expand "Sym" )"1" (expand "fullset" )"1" (expand "star_closed?" )"1" (skosimp*)"1" (expand "op" )"1" (expand "member" )"1" (propax) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "identity" )"2" (expand "member" )"2" (expand "Sym" )"2" (expand "fullset" ) (("2" (propax) nil nil ))nil ))nil ))nil ))nil )"3" (expand "restrict" )"3" (expand "identity?" )"3" (skosimp*)"3" (expand "op" )"3" (expand "restrict" )"3" (expand "identity" )"3" (expand "o" )"3" (prop)"1" nil nil )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (grind)"2" (expand "o" 1 1)"2" (expand "o" 1 1)"2" (expand "o" 1 1)"2" (expand "o" 1 1) (("2" (propax) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "comp_inverse_right[(S),(S)]" )"1" (expand "inv_exists?" )"1" (skosimp*)"1" (inst?)"1" (assert )"1" (expand "op" )"1" (expand "restrict" )"1" (expand "O" )"1" (assert )"1" (typepred "x!1" )"1" (inst + "inverse(x!1)" )"1" (expand "identity" )"1" "comp_inverse_right[(S),(S)]" )"1" "1" "1" "1" "1" "1" )"1" "1" (grind) nil nil ))nil ))nil ))nil ))nil )"2" "1" "comp_inverse_left[(S),(S)]" )"1" (inst?) nil nil ))nil )"2" "2" "1" )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "Sym" )"2" expand "fullset" )"2" (propax) nil nil ))nil ))nil )"3" (inst + "1" )"3" "3" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (inst + "1" ) (("2" (hide 2) (("2" (grind) nil nil )) nil ))nil ))nil ))nil ))nil )"set" sets nil )"bool" sets nil )"[perm, perm -> perm]" symmetric_groups nil )"bool" groupoid_def nil )"set[perm]" symmetric_groups nil )identity const-decl "(bijective?[T, T])" identity nil )identity ? const-decl "bool" operator_defs nil )"set[posnat]" symmetric_groups nil )set type-eq-decl nil sets nil )nil integers nil )"bool" reals nil )nil integers nil )"bool" reals nil )nil booleans nil )nil integers nil )"[rational -> boolean]" integers nil )nil rationals nil )"[real -> boolean]" rationals nil )nil reals nil )"[number_field -> boolean]" reals nil )nil number_fields nil )"[number -> boolean]" number_fieldsnil )nil booleans nil )nil numbers nil )"bool" functions nil )nil symmetric_groups nil )"T3" function_props nil )"R" restrict nil )"bool" monad_def nil )"(injective?[T1, T3])" nil )"(surjective?[T1, T3])" function_props nil )"(bijective?[T1, T3])" nil )"bool" functions nil )"bool" functions nil )NOT const-decl "[bool -> bool]" booleans nil )"bool" operator_defs nil )"bool" monoid_def nil )"bool" group_def nil )"{x: D | f(x) = y}" nil )nil function_inverse nil )"(total_order?[real])" nil )"R" extend nil )"(Sym)" symmetric_groups nil )"D" function_inverse nil )"(bijective?[R, D])" function_inverse nil )"bool" booleans nil )nil function_inverse nil )"bool" group_def nil ))nil )nil 3374416353"" (expand "group?" )"" (prop)"1" (expand "monoid?" )"1" (prop)"1" (expand "monad?" )"1" (prop)"1" (expand "groupoid?" )"1" (expand "Sym" )"1" (expand "fullset" )"1" (expand "star_closed?" )"1" (skosimp*)"1" (expand "op" )"1" (expand "member" )"1" (propax) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "identity" )"2" (expand "member" )"2" (expand "Sym" )"2" (expand "fullset" ) (("2" (propax) nil nil ))nil ))nil ))nil ))nil )"3" (expand "restrict" )"3" (expand "identity?" )"3" (skosimp*)"3" (expand "op" )"3" (expand "restrict" )"3" (expand "identity" )"3" (expand "o" )"3" (prop)"1" nil nil )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (grind)"2" (expand "o" 1 1)"2" (expand "o" 1 1)"2" (expand "o" 1 1)"2" (expand "o" 1 1) (("2" (propax) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (lemma "comp_inv_right[(S),(S)]" )"1" (expand "inv_exists?" )"1" (skosimp*)"1" (inst?)"1" (assert )"1" (expand "op" )"1" (expand "restrict" )"1" (expand "O" )"1" (assert )"1" (typepred "x!1" )"1" (inst + "inv(x!1)" )"1" (expand "identity" )"1" "comp_inv_right[(S),(S)]" )"1" "1" "1" "1" "1" "1" )"1" "1" (grind) nil nil ))nil ))nil ))nil ))nil )"2" "1" "comp_inv_left[(S),(S)]" )"1" (inst?) nil nil ))nil )"2" "2" "1" )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "Sym" )"2" expand "fullset" )"2" (propax) nil nil ))nil ))nil )"3" (inst + "1" )"3" "3" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (inst + "1" ) (("2" (hide 2) (("2" (grind) nil nil )) nil ))nil ))nil ))nil ))nil )"bool" group_def nil )"bool" group_def nil )"bool" monoid_def nil )"bool" monad_def nil )"bool" groupoid_def nil ))nil )nil 3251123754"" (expand "group?" )"" (prop)"1" (expand "monoid?" )"1" (prop)"1" (expand "monad?" )"1" (prop)"1" (expand "groupoid?" )"1" (expand "Sym" )"1" (expand "fullset" )"1" (expand "star_closed?" )"1" (skosimp*)"1" (expand "op" )"1" (expand "member" )"1" (propax) nil nil )) nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "identity" )"2" (expand "member" )"2" (expand "Sym" )"2" (expand "fullset" ) (("2" (propax) nil nil ))nil ))nil ))nil ))nil )"3" (expand "restrict" )"3" (expand "identity?" )"3" (skosimp*)"3" (expand "op" )"3" (expand "restrict" )"3" (expand "identity" )"3" (expand "o" )"3" (prop)"1" nil nil )"2" nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (grind)"2" (expand "o" ) (("2" (propax) nil nil )) nil )) nil ))nil ))nil )"2" (lemma "comp_inv_right[(S),(S)]" )"1" (expand "inv_exists?" )"1" (skosimp*)"1" (inst?)"1" (assert )"1" (expand "op" )"1" (expand "restrict" )"1" (expand "O" )"1" (assert )"1" (typepred "x!1" )"1" (inst + "inv(x!1)" )"1" (expand "identity" )"1" "comp_inv_right[(S),(S)]" )"1" "1" "1" "1" "1" "1" )"1" "1" (grind) nil nil ))nil ))nil ))nil ))nil )"2" "1" "comp_inv_left[(S),(S)]" )"1" (inst?) nil nil ))nil )"2" "2" "1" )"2" "2" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (expand "Sym" )"2" expand "fullset" )"2" (propax) nil nil ))nil ))nil )"3" (inst + "1" )"3" "3" (grind) nil nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil ))nil )"2" (inst + "1" ) (("2" (hide 2) (("2" (grind) nil nil )) nil ))nil ))nil ))nil ))nil )"bool" groupoid_def nil )"bool" monad_def nil )"bool" monoid_def nil )"bool" group_def nil )"bool" group_def nil ))nil )))quality 100%
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2026-03-28
