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(* const-decl "set[T]" cosets nil)
(normal_subgroup? const-decl "boolean" normal_subgroups nil))
nil))
(lc_gen_normal_TCC2 0
(lc_gen_normal_TCC2-1 nil 3406564260
("" (skosimp*) (("" (inst + "a!1") nil nil)) nil)
((T formal-nonempty-type-decl nil normal_subgroups nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(set type-eq-decl nil sets nil)
(* formal-const-decl "[T, T -> T]" normal_subgroups nil)
(one formal-const-decl "T" normal_subgroups nil)
(group? const-decl "bool" group_def nil)
(group nonempty-type-eq-decl nil group nil)
(a!1 skolem-const-decl "T" normal_subgroups nil)
(G!1 skolem-const-decl "group[T, *, one]" normal_subgroups nil))
nil))
(lc_gen_normal 0
(lc_gen_normal-1 nil 3406564267
("" (skosimp*)
(("" (lemma "lc_gen_def")
(("" (inst?)
(("" (assert)
(("" (expand "normal_subgroup?")
(("" (flatten)
(("" (assert)
(("" (name "aa" "lc_gen(G!1, H!1, a!1 * H!1)")
(("" (replace -1)
(("" (lemma "lc_eq")
(("" (inst - "G!1" "H!1" "aa" "a!1")
(("" (assert)
(("" (skosimp*)
(("" (replace -1)
((""
(inst + "a!1*h!1*inv(a!1)")
(("1"
(rewrite "associative")
(("1"
(rewrite "associative")
(("1"
(rewrite "associative")
(("1"
(rewrite "inv_left")
(("1"
(rewrite "one_right")
nil
nil))
nil))
nil))
nil))
nil)
("2"
(lemma "nsg_prop")
(("2"
(inst?)
(("2"
(inst - "G!1" "H!1")
(("2" (assert) nil nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((one formal-const-decl "T" normal_subgroups nil)
(* formal-const-decl "[T, T -> T]" normal_subgroups nil)
(T formal-nonempty-type-decl nil normal_subgroups nil)
(lc_gen_def formula-decl nil cosets nil)
(lc_gen const-decl "{a: T | G(a) AND lc = a * H}" cosets nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(left_cosets type-eq-decl nil cosets nil)
(subgroup? const-decl "bool" group_def nil)
(* const-decl "set[T]" cosets nil)
(subgroup type-eq-decl nil group nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(lc_eq formula-decl nil cosets nil)
(nsg_prop formula-decl nil normal_subgroups nil)
(normal_subgroup type-eq-decl nil normal_subgroups nil)
(associative formula-decl nil semigroup nil)
(one_right formula-decl nil group nil)
(inv_left formula-decl nil group nil)
(inv const-decl "{y | x * y = one AND y * x = one}" group nil)
(h!1 skolem-const-decl "(H!1)" normal_subgroups nil)
(a!1 skolem-const-decl "T" normal_subgroups nil)
(H!1 skolem-const-decl "group[T, *, one]" normal_subgroups nil)
(normal_subgroup? const-decl "boolean" normal_subgroups nil)
(group nonempty-type-eq-decl nil group nil)
(group? const-decl "bool" group_def nil)
(set type-eq-decl nil sets nil)
(bool nonempty-type-eq-decl nil booleans nil)
(boolean nonempty-type-decl nil booleans nil))
nil))
(abelian_normal 0
(abelian_normal-1 nil 3406306875
("" (skosimp*)
(("" (expand "normal_subgroup?")
(("" (assert)
(("" (skosimp*)
(("" (expand "subset?")
(("" (skosimp*)
(("" (assert)
(("" (expand "*")
(("" (skosimp*)
(("" (replace -3)
(("" (typepred "h!1")
(("" (skosimp*)
(("" (typepred "h!2")
(("" (replace -2)
((""
(hide -2)
((""
(hide -4)
((""
(expand "abelian_group?")
((""
(expand "commutative?")
((""
(expand "restrict")
((""
(inst -2 "h!2" "a!1")
(("1"
(rewrite "associative")
(("1"
(replace -2)
(("1"
(rewrite "assoc")
(("1"
(rewrite "inv_left")
(("1"
(rewrite
"one_left")
nil
nil))
nil))
nil))
nil))
nil)
("2"
(hide 2)
(("2"
(expand "subgroup?")
(("2"
(expand "subset?")
(("2"
(inst?)
(("2"
(assert)
nil
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil))
nil)
((normal_subgroup? const-decl "boolean" normal_subgroups nil)
(* const-decl "set[T]" cosets nil)
(* const-decl "set[T]" cosets nil)
(commutative? const-decl "bool" operator_defs nil)
(G!1 skolem-const-decl "group[T, *, one]" normal_subgroups nil)
(H!1 skolem-const-decl "group[T, *, one]" normal_subgroups nil)
(h!2 skolem-const-decl "(H!1)" normal_subgroups nil)
(assoc formula-decl nil group nil)
(inv_left formula-decl nil group nil)
(one_left formula-decl nil group nil)
(associative formula-decl nil semigroup nil)
(subgroup? const-decl "bool" group_def nil)
(restrict const-decl "R" restrict nil)
(abelian_group? const-decl "bool" group_def nil)
(boolean nonempty-type-decl nil booleans nil)
(bool nonempty-type-eq-decl nil booleans nil)
(NOT const-decl "[bool -> bool]" booleans nil)
(T formal-nonempty-type-decl nil normal_subgroups nil)
(set type-eq-decl nil sets nil)
(* formal-const-decl "[T, T -> T]" normal_subgroups nil)
(one formal-const-decl "T" normal_subgroups nil)
(group? const-decl "bool" group_def nil)
(group nonempty-type-eq-decl nil group nil)
(= const-decl "[T, T -> boolean]" equalities nil)
(AND const-decl "[bool, bool -> bool]" booleans nil)
(inv const-decl "{y | x * y = one AND y * x = one}" group nil)
(member const-decl "bool" sets nil)
(subset? const-decl "bool" sets nil))
shostak)))
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