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(associative formula-decl nil semigroup "algebra/")
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(inv_right formula-decl nil group "algebra/")
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(H!1 skolem-const-decl "subgroup[T, *, one](G!1)" right_left_cosets
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(h!2 skolem-const-decl "(H!1)" right_left_cosets nil)
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(h!3 skolem-const-decl "(H!1)" right_left_cosets nil)
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(* formal-const-decl "[T, T -> T]" right_left_cosets nil)
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(* const-decl "set[T]" cosets "algebra/")
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nil)
(H!1 skolem-const-decl "subgroup[T, *, one](G!1)" right_left_cosets
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(left_cosets const-decl "setofsets[T]" right_left_cosets nil)
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(G!1 skolem-const-decl "finite_group[T, *, one]" right_left_cosets
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(b!1 skolem-const-decl "(left_cosets(G!1, H!1))" right_left_cosets
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(left_cosets type-eq-decl nil cosets "algebra/")
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(left_cosets_disjoint formula-decl nil right_left_cosets nil)
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(left_coset const-decl "{s: set[T] | subset?(s, G)}" cosets
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(H!1 skolem-const-decl "subgroup[T, *, one](G!1)" right_left_cosets
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(G!1 skolem-const-decl "group[T, *, one]" right_left_cosets nil)
(one_left formula-decl nil group "algebra/")
(one_in formula-decl nil monad "algebra/")
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(member const-decl "bool" sets nil)
(star_closed formula-decl nil groupoid "algebra/")
(star_closed? const-decl "bool" groupoid_def "algebra/")
(groupoid nonempty-type-eq-decl nil groupoid "algebra/")
(* const-decl "set[T]" cosets "algebra/")
(NOT const-decl "[bool -> bool]" booleans nil))
shostak))
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((H!1 skolem-const-decl "group[T, *, one]" right_left_cosets nil)
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(* const-decl "set[T]" cosets "algebra/")
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(rc_gen const-decl "{a: T | G(a) AND rc = H * a}" cosets
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(right_cosets type-eq-decl nil cosets "algebra/")
(inv const-decl "{y | x * y = one AND y * x = one}" group
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(* const-decl "set[T]" cosets "algebra/")
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(lc_eq formula-decl nil cosets "algebra/")
(divby formula-decl nil group "algebra/")
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(inv_star formula-decl nil group "algebra/")
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(surjective? const-decl "bool" functions nil)
(bijective? const-decl "bool" functions nil)
(A!1 skolem-const-decl "(right_cosets(G!1, H!1))" right_left_cosets
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shostak))
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(group nonempty-type-eq-decl nil group "algebra/")
(group? const-decl "bool" group_def "algebra/")
(subgroup? const-decl "bool" group_def "algebra/")
(subgroup type-eq-decl nil group "algebra/")
(setofsets type-eq-decl nil sets nil)
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(finite_group? const-decl "bool" group_def "algebra/")
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shostak))
(divide_TCC1 0
(divide_TCC1-1 nil 3530434541
("" (skosimp*)
(("" (inst 1 "one")
(("1" (rewrite "left_coset_one") nil nil)
("2" (rewrite "one_in") nil nil))
nil))
nil)
((G!1 skolem-const-decl "group[T, *, one]" right_left_cosets nil)
(group nonempty-type-eq-decl nil group "algebra/")
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(bool nonempty-type-eq-decl nil booleans nil)
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(T formal-type-decl nil right_left_cosets nil)
(normal_subgroup type-eq-decl nil normal_subgroups "algebra/")
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(left_coset_one formula-decl nil cosets "algebra/")
(monad nonempty-type-eq-decl nil monad "algebra/")
(monad? const-decl "bool" monad_def "algebra/")
(one_in formula-decl nil monad "algebra/"))
nil))
(divide_TCC2 0
(divide_TCC2-1 nil 3530434541
("" (skosimp*) (("" (rewrite "left_cosets_group[T,*,one]") nil nil))
nil)
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(T formal-type-decl nil right_left_cosets nil)
(* formal-const-decl "[T, T -> T]" right_left_cosets nil)
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nil))
(divide_TCC3 0
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("" (skosimp*)
(("" (inst 1 "N!1")
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nil))
nil))
nil)
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(= const-decl "[T, T -> boolean]" equalities nil)
(* const-decl "set[T]" cosets "algebra/")
(normal_subgroup? const-decl "boolean" normal_subgroups "algebra/")
(normal_subgroup type-eq-decl nil normal_subgroups "algebra/")
(left_cosets type-eq-decl nil cosets "algebra/")
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right_left_cosets nil)
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(monad nonempty-type-eq-decl nil monad "algebra/")
(monad? const-decl "bool" monad_def "algebra/")
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(left_coset_one formula-decl nil cosets "algebra/"))
nil))
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(("" (expand "normal_subgroup?") (("" (assert) nil nil)) nil))
nil))
nil)
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(one formal-const-decl "T" right_left_cosets nil)
(* formal-const-decl "[T, T -> T]" right_left_cosets nil)
(set type-eq-decl nil sets nil)
(T formal-type-decl nil right_left_cosets nil)
(NOT const-decl "[bool -> bool]" booleans nil)
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(boolean nonempty-type-decl nil booleans nil))
nil))
(divide_TCC5 0
(divide_TCC5-1 nil 3530434541
("" (skosimp*)
(("" (expand "group?")
(("" (prop)
(("1" (expand "monoid?")
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(("1" (expand "monad?")
(("1" (prop)
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(("1" (assert)
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(("1" (expand "left_cosets")
--> --------------------
--> maximum size reached
--> --------------------
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