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((subgroup? const-decl "bool" group_def "algebra/" )
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(inv const-decl "{y | x * y = one AND y * x = one}" group
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(/ const-decl "group[left_cosets(G, N), mult(G, N), N]"
right_left_cosets nil )
(subset? const-decl "bool" sets nil )
(member const-decl "bool" sets nil ))
shostak))
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nil ))
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nil ))
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nil ))
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nil )
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nil ))
nil ))
nil ))
nil )
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nil ))
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(lemma
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(inst
-1
"G!1"
"prod[T1, *, one1](N!1, H!1)"
"N!1" )
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nil )
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nil ))
nil )
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nil )
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nil ))
nil ))
nil ))
nil ))
nil )
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nil ))
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nil ))
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nil )
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nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
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nil ))
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nil ))
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nil )
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nil )
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nil ))
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(lemma
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(inst
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nil )
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nil )
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nil ))
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(typepred
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nil ))
nil ))
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nil ))
nil ))
nil )
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nil )
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sets_lemmas nil )
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nil ))
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(* formal-const-decl "[T1, T1 -> T1]" isomorphism_theorems nil )
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nil ))
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nil ))
nil ))
nil ))
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sets_lemmas nil )
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nil )
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nil ))
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"varphi!1" )
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(case-replace "extend
[left_cosets[T1, *, one1](prod[T1, *, one1](N!1, H!1), N!1),
(prod[T1, *, one1](N!1, H!1) / N!1), bool, FALSE]
(image(varphi!1, restrict[T1, (H!1), bool](H!1))) = prod[T1, *, one1](N!1, H!1) / N!1")
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(lemma
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(("1"
(inst
-1
"H!1"
"prod[T1, *, one1](N!1, H!1) / N!1"
"varphi!1" )
(("1" (assert ) nil nil ))
nil ))
nil ))
nil )
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(expand "isomorphic?" )
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(inst 1 "phi!1" )
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(expand "homomorphism?" )
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(skosimp*)
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(inst -1 "a!1" "b!1" )
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(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
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(inst
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"G!1"
"prod[T1, *, one1](N!1, H!1)"
"N!1" )
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nil ))
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nil ))
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nil
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(typepred "N!1" )
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"G!1"
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(expand *
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nil
nil ))
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(lemma "H_K_are_subgroups[T1, *, one1]" )
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(prop)
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(lemma
"normal_subgroup_tran[T1, *, one1]" )
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(inst
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(* const-decl "set[T]" cosets "algebra/" )
(left_cosets type-eq-decl nil cosets "algebra/" )
(mult const-decl "left_cosets(G, H)" factor_groups "algebra/" )
(fullset const-decl "set" sets nil )
(IFF const-decl "[bool, bool -> bool]" booleans nil )
(isomorphic? const-decl "bool" homomorphisms "algebra/" )
(/ const-decl "group[left_cosets(G, N), mult(G, N), N]"
right_left_cosets nil )
(member const-decl "bool" sets nil )
(monad? const-decl "bool" monad_def "algebra/" )
(monoid? const-decl "bool" monoid_def "algebra/" )
(left_coset_one formula-decl nil cosets "algebra/" )
(HK_subgroup_permute formula-decl nil products_subgroups nil )
(H_K_are_subgroups formula-decl nil products_subgroups nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(normal_subgroup_tran formula-decl nil groups_scaf nil )
(G_TCC1 assuming-tcc nil isomorphism_theorems nil )
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil )
(HK_subgroup formula-decl nil products_subgroups nil )
(left_cosets_group formula-decl nil factor_groups "algebra/" )
(homomorphism type-eq-decl nil homomorphisms "algebra/" )
(homomorphism? const-decl "bool" homomorphisms "algebra/" )
(surjective? const-decl "bool" functions nil )
(x!2 skolem-const-decl "(H!1)" isomorphism_theorems nil )
(x!1 skolem-const-decl
"left_cosets[T1, *, one1](prod[T1, *, one1](N!1, H!1), N!1)"
isomorphism_theorems nil )
(H!1 skolem-const-decl "subgroup[T1, *, one1](G!1)"
isomorphism_theorems nil )
(N!1 skolem-const-decl "normal_subgroup[T1, *, one1](G!1)"
isomorphism_theorems nil )
(G!1 skolem-const-decl "group[T1, *, one1]" isomorphism_theorems
nil )
(kernel_normal formula-decl nil homomorphism_lemmas nil )
(isomorphism? const-decl "bool" homomorphisms "algebra/" )
(FALSE const-decl "bool" booleans nil )
(extend const-decl "R" extend nil )
(image const-decl "set[R]" function_image nil )
(restrict const-decl "R" restrict nil )
(first_isomorphism_th formula-decl nil homomorphism_lemmas nil )
(second_isomorphism_th_aux formula-decl nil isomorphism_theorems
nil ))
shostak))
(third_isomorphism_th_aux_TCC1 0
(third_isomorphism_th_aux_TCC1-1 nil 3524797530
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(* formal-const-decl "[T1, T1 -> T1]" isomorphism_theorems nil )
(set type-eq-decl nil sets nil )
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(normal_subgroup type-eq-decl nil normal_subgroups "algebra/" )
(normal_subgroup? const-decl "boolean" normal_subgroups "algebra/" )
(left_coset_one formula-decl nil cosets "algebra/" )
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(monad? const-decl "bool" monad_def "algebra/" )
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(monoid? const-decl "bool" monoid_def "algebra/" ))
nil ))
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(bool nonempty-type-eq-decl nil booleans nil )
(set type-eq-decl nil sets nil )
(group? const-decl "bool" group_def "algebra/" )
(group nonempty-type-eq-decl nil group "algebra/" )
(normal_subgroup? const-decl "boolean" normal_subgroups "algebra/" )
(normal_subgroup type-eq-decl nil normal_subgroups "algebra/" )
(T1 formal-type-decl nil isomorphism_theorems nil )
(* formal-const-decl "[T1, T1 -> T1]" isomorphism_theorems nil )
(one1 formal-const-decl "T1" isomorphism_theorems nil ))
nil ))
(third_isomorphism_th_aux_TCC3 0
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(group? const-decl "bool" group_def "algebra/" )
(group nonempty-type-eq-decl nil group "algebra/" )
(normal_subgroup? const-decl "boolean" normal_subgroups "algebra/" )
(normal_subgroup type-eq-decl nil normal_subgroups "algebra/" )
(T1 formal-type-decl nil isomorphism_theorems nil )
(* formal-const-decl "[T1, T1 -> T1]" isomorphism_theorems nil )
(one1 formal-const-decl "T1" isomorphism_theorems nil ))
nil ))
(third_isomorphism_th_aux 0
(third_isomorphism_th_aux-1 nil 3524915806
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shostak))
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nil ))
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nil ))
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((""
(lemma
"first_isomorphism_th[left_cosets[T1, *, one1](G!1, N!1), mult(G!1, N!1), N!1, left_cosets[T1, *, one1](G!1, M!1), mult(G!1, M!1), M!1]" )
(("1" (inst -1 "G!1 / N!1" "G!1 / M!1" "psi!1" )
(("1" (replace -4 -1)
(("1" (assert )
(("1"
(case-replace "extend
[left_cosets[T1, *, one1](G!1, M!1), (G!1 / M!1), bool,
FALSE]
(image(psi!1,
restrict
[left_cosets[T1, *, one1](G!1, N!1), (G!1 / N!1),
bool]
(G!1 / N!1))) = G!1 / M!1" :hide? T)
(("1" (assert )
(("1" (hide (-1 -2 -3))
(("1"
(lemma
"kernel_normal[left_cosets[T1, *, one1](G!1, N!1), mult[T1, *, one1](G!1, N!1),
N!1, left_cosets[T1, *, one1](G!1, M!1), mult[T1, *, one1](G!1, M!1),
M!1]")
(("1"
(inst -1 "/[T1, *, one1](G!1, N!1)"
"/[T1, *, one1](G!1, M!1)" "psi!1" )
(("1" (assert ) nil nil )) nil ))
nil ))
nil ))
nil )
("2" (hide (-1 -4 2))
(("2" (decompose-equality 1)
(("2" (expand "extend" )
(("2" (lift-if)
(("2"
(prop)
(("2"
(expand "image" )
(("2"
(expand "surjective?" )
(("2"
(inst -3 "x!1" )
(("2"
(skosimp)
(("2"
(inst 1 "x!2" )
(("1" (assert ) nil nil )
("2"
(expand "restrict" )
(("2" (propax) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide-all-but 1)
(("2" (rewrite "left_cosets_group[T1, *, one1]" ) nil
nil ))
nil )
("3" (hide-all-but 1)
(("3" (rewrite "left_cosets_group[T1, *, one1]" ) nil
nil ))
nil )
("4" (hide-all-but 1)
(("4" (inst 1 "one1" )
(("1" (rewrite "left_coset_one[T1,*,one1]" ) nil nil )
("2" (typepred "G!1" )
(("2"
(expand * "group?" "monoid?" "monad?" "member" )
(("2" (flatten) nil nil )) nil ))
nil ))
nil ))
nil )
("5" (hide-all-but 1)
(("5" (inst 1 "one1" )
(("1" (rewrite "left_coset_one[T1,*,one1]" ) nil nil )
("2" (typepred "G!1" )
(("2"
(expand * "group?" "monoid?" "monad?" "member" )
(("2" (flatten) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
((third_isomorphism_th_aux formula-decl nil isomorphism_theorems
nil )
(mult const-decl "left_cosets(G, H)" factor_groups "algebra/" )
(left_cosets type-eq-decl nil cosets "algebra/" )
(* const-decl "set[T]" cosets "algebra/" )
(= const-decl "[T, T -> boolean]" equalities nil )
(first_isomorphism_th formula-decl nil homomorphism_lemmas nil )
(fullset const-decl "set" sets nil )
(FALSE const-decl "bool" booleans nil )
(extend const-decl "R" extend nil )
(image const-decl "set[R]" function_image nil )
(restrict const-decl "R" restrict nil )
(kernel_normal formula-decl nil homomorphism_lemmas nil )
(G!1 skolem-const-decl "group[T1, *, one1]" isomorphism_theorems
nil )
(M!1 skolem-const-decl "normal_subgroup[T1, *, one1](G!1)"
isomorphism_theorems nil )
(x!1 skolem-const-decl "left_cosets[T1, *, one1](G!1, M!1)"
isomorphism_theorems nil )
(N!1 skolem-const-decl "normal_subgroup[T1, *, one1](G!1)"
isomorphism_theorems nil )
(x!2 skolem-const-decl "(G!1 / N!1)" isomorphism_theorems nil )
(surjective? const-decl "bool" functions nil )
(homomorphism type-eq-decl nil homomorphisms "algebra/" )
(homomorphism? const-decl "bool" homomorphisms "algebra/" )
(/ const-decl "group[left_cosets(G, N), mult(G, N), N]"
right_left_cosets nil )
(left_cosets_group formula-decl nil factor_groups "algebra/" )
(left_coset_one formula-decl nil cosets "algebra/" )
(monoid? const-decl "bool" monoid_def "algebra/" )
(member const-decl "bool" sets nil )
(monad? const-decl "bool" monad_def "algebra/" )
(NOT const-decl "[bool -> bool]" booleans nil )
(normal_subgroup type-eq-decl nil normal_subgroups "algebra/" )
(normal_subgroup? const-decl "boolean" normal_subgroups "algebra/" )
(group nonempty-type-eq-decl nil group "algebra/" )
(group? const-decl "bool" group_def "algebra/" )
(one1 formal-const-decl "T1" isomorphism_theorems nil )
(* formal-const-decl "[T1, T1 -> T1]" isomorphism_theorems 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 isomorphism_theorems nil ))
shostak))
(correspondence_theorem 0
(correspondence_theorem-1 nil 3530907884
("" (skosimp*)
((""
(inst 1
"LAMBDA (N: subgroup_contain(G!1, kernel(G!1, GP!1)(f!1))): image(f!1, N)" )
(("1" (prop)
(("1" (expand "bijective?" )
(("1" (prop)
(("1" (expand "injective?" )
(("1" (skosimp*)
(("1" (typepred "x1!1" "x2!1" )
(("1" (hide (-1 -4))
(("1"
(lemma
"homo_inv_image_image_cor[T1,*,one1,T2,o,one2]" )
(("1" (assert )
(("1" (expand "subgroup?" -1)
(("1" (inst-cp -1 "G!1" "GP!1" "f!1" "x2!1" )
(("1" (inst -1 "G!1" "GP!1" "f!1" "x1!1" )
(("1"
(assert )
(("1"
(decompose-equality -1)
(("1"
(decompose-equality -2)
(("1"
(decompose-equality -7)
(("1"
(decompose-equality 1)
(("1"
(iff)
(("1"
(prop)
(("1"
(inst -3 "x!1" )
(("1"
(inst -4 "x!1" )
(("1"
(iff)
(("1"
(prop)
(("1"
(hide-all-but
(-4 1))
(("1"
(expand
"restrict" )
(("1"
(propax)
nil
nil ))
nil ))
nil )
("2"
(hide-all-but
(-3 1))
(("2"
(expand
"restrict" )
(("2"
(propax)
nil
nil ))
nil ))
nil )
("3"
(hide (-2 1 3))
(("3"
(expand
"inverse_image" )
(("3"
(expand
"member" )
(("3"
(inst?)
(("3"
(expand
"extend" )
(("3"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("4"
(hide-all-but
(-1 1))
(("4"
(expand
"restrict" )
(("4"
(propax)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but
(-1 -4 1))
(("2"
(expand *
"subgroup?"
"subset?"
"member" )
(("2"
(inst?)
(("2"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(inst -3 "x!1" )
(("1"
(inst -4 "x!1" )
(("1"
(iff)
(("1"
(prop)
(("1"
(hide-all-but
(-2 1))
(("1"
(expand
"restrict" )
(("1"
(propax)
nil
nil ))
nil ))
nil )
("2"
(hide (-2 1 3))
(("2"
(expand
"inverse_image" )
(("2"
(expand
"member" )
(("2"
(inst?)
(("2"
(expand
"extend" )
(("2"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("3"
(hide-all-but
(-3 1))
(("3"
(expand
"restrict" )
(("3"
(propax)
nil
nil ))
nil ))
nil )
("4"
(hide-all-but
(-1 3))
(("4"
(expand
"restrict" )
(("4"
(propax)
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2"
(hide-all-but
(-1 -6 1))
(("2"
(expand *
"subgroup?"
"subset?"
"member" )
(("2"
(inst?)
(("2"
(assert )
nil
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (rewrite "T2_is_group" ) nil nil )
("3" (rewrite "T1_is_group" ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (expand "surjective?" )
(("2" (skosimp*)
(("2" (inst 1 "inverse_image(f!1, y!1)" )
(("1" (decompose-equality 1)
(("1" (iff)
(("1" (prop)
(("1" (expand "extend" )
(("1" (prop)
(("1" (expand "image" )
(("1"
(skosimp)
(("1"
(typepred "x!2" )
(("1"
(expand "restrict" )
(("1"
(expand "inverse_image" )
(("1"
(expand "member" )
(("1" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (expand "extend" )
(("2" (prop)
(("1" (expand "image" )
(("1"
(inst?)
(("1"
(skosimp)
(("1"
(inst 1 "x!2" )
(("1" (assert ) nil nil )
("2"
(expand "restrict" )
(("2"
(expand "inverse_image" )
(("2"
(expand "member" )
(("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide -2)
(("2"
(typepred "y!1" )
(("2"
(hide -1)
(("2"
(expand *
"subgroup?"
"subset?"
"member" )
(("2"
(inst?)
(("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide -1)
(("2" (lemma "homo_inv_image[T1,*,one1,T2,o,one2]" )
(("1" (inst?)
(("1" (assert )
(("1" (prop)
(("1"
(lemma "subgroup_is_group[T1, *, one1]" )
(("1"
(inst?)
(("1" (assert ) nil nil ))
nil ))
nil )
("2"
(lemma
"kernel_in_inv_image[T1,*,one1,T2,o,one2]" )
(("2"
(inst?)
(("2" (assert ) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide 2)
(("2" (rewrite "T2_is_group" ) nil nil )) nil )
("3" (hide 2)
(("3" (rewrite "T1_is_group" ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (skosimp*)
(("2" (prop)
(("1" (lemma "homo_image[T1,*,one1,T2,o,one2]" )
(("1" (inst?) nil nil )
("2" (hide-all-but 1)
(("2" (rewrite "T2_is_group" ) nil nil )) nil )
("3" (hide-all-but 1)
(("3" (rewrite "T1_is_group" ) nil nil )) nil ))
nil )
("2" (lemma "homo_inv_image[T1,*,one1,T2,o,one2]" )
(("1"
(inst -1 "G!1" "GP!1" "f!1"
"image(f!1, restrict[T1, (G!1), boolean](N!1))" )
(("1"
(lemma
"homo_inv_image_image_cor[T1, *, one1,T2, o, one2]" )
(("1" (inst?) (("1" (assert ) nil nil )) nil )) nil )
("2" (prop)
(("2" (hide (-2 2))
(("2" (lemma "subgroup_is_group[T2, o, one2]" )
(("2" (inst?) (("2" (assert ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide-all-but 1)
(("2" (rewrite "T2_is_group" ) nil nil )) nil )
("3" (hide-all-but 1)
(("3" (rewrite "T1_is_group" ) nil nil )) nil ))
nil )
("3" (lemma "homo_image_normal[T1,*,one1,T2,o,one2]" )
(("1" (inst?) (("1" (assert ) nil nil )) nil )
("2" (hide-all-but 1)
(("2" (rewrite "T2_is_group" ) nil nil )) nil )
("3" (hide-all-but 1)
(("3" (rewrite "T1_is_group" ) nil nil )) nil ))
nil )
("4" (lemma "homo_inv_image_normal[T1,*,one1,T2,o,one2]" )
(("1"
(inst -1 "G!1" "GP!1" "f!1"
"image(f!1, restrict[T1, (G!1), boolean](N!1))" )
(("1"
(lemma
"homo_inv_image_image_cor[T1, *, one1,T2, o, one2]" )
(("1" (inst?)
(("1" (assert )
(("1" (prop)
(("1" (hide (-2 -4 -5))
(("1" (expand "normal_subgroup?" )
(("1" (flatten)
(("1"
(skosimp)
(("1"
(hide -2)
(("1"
(expand * "subset?" "member" )
(("1"
(skosimp)
(("1"
(decompose-equality -1)
(("1"
(inst -1 "x!1" )
(("1"
(iff)
(("1"
(prop)
(("1"
(hide-all-but (-2 1))
(("1"
(expand "restrict" )
(("1"
(propax)
nil
nil ))
nil ))
nil )
("2"
(hide (1 3))
(("2"
(expand
"inverse_image" )
(("2"
(expand "member" )
(("2"
(expand "image" )
(("2"
(inst -1 "a!1" )
(("2"
(inst
-1
"x!1" )
(("2"
(prop)
(("1"
(expand
"extend" )
(("1"
(prop)
nil
nil ))
nil )
("2"
(hide 2)
(("2"
(expand
"*" )
(("2"
(skosimp)
(("2"
(typepred
"h!1" )
(("2"
(skosimp)
(("2"
(replaces
-1)
(("2"
(inst
1
"inv[T1, *, one1](a!1) * h!2" )
(("2"
(inst
1
"h!2" )
(("2"
(expand
"extend" )
(("2"
(prop)
(("1"
(inst?)
(("1"
(assert )
(("1"
(expand
"restrict" )
(("1"
(propax)
nil
nil ))
nil ))
nil ))
nil )
("2"
(hide
-1)
(("2"
(typepred
"h!2"
"N!1" )
(("2"
(hide
(-2
-4))
(("2"
(expand *
"subgroup?"
"subset?"
"member" )
(("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 )
("2"
(hide (-1 2))
(("2"
(expand "*" )
(("2"
(skosimp)
(("2"
(typepred "h!1" )
(("2"
(skosimp)
(("2"
(replaces -1)
(("2"
(replaces -1)
(("2"
(rewrite
"product_in[T1, *, one1]" )
(("2"
(hide 2)
(("2"
(rewrite
"product_in[T1, *, one1]" )
(("1"
(hide
2)
(("1"
(rewrite
"inv_in" )
nil
nil ))
nil )
("2"
(hide
2)
(("2"
(typepred
"h!2"
"N!1" )
(("2"
(hide
(-2
-4))
(("2"
(expand *
"subgroup?"
"subset?"
"member" )
(("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 )
("2" (hide-all-but 1)
(("2" (typepred "N!1" )
(("2" (hide (-1 -2))
(("2"
(expand "subgroup?" )
(("2" (propax) nil nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil ))
nil )
("2" (hide-all-but 1)
(("2" (rewrite "T2_is_group" ) nil nil )) nil )
("3" (hide-all-but 1)
(("3" (rewrite "T1_is_group" ) nil nil )) nil ))
nil ))
nil ))
nil ))
nil )
("2" (skosimp*)
(("2" (lemma "homo_image[T1,*,one1,T2,o,one2]" )
(("1" (inst?)
(("1" (assert )
(("1" (hide -2)
(("1" (lemma "subgroup_is_group[T2, o, one2]" )
(("1" (inst?) (("1" (assert ) nil nil )) nil )) nil ))
nil ))
nil ))
nil )
("2" (hide 2) (("2" (rewrite "T2_is_group" ) nil nil )) nil )
("3" (hide 2) (("3" (rewrite "T1_is_group" ) nil nil )) nil ))
nil ))
nil )
("3" (rewrite "T1_is_group" ) nil nil ))
nil ))
nil )
((fullset const-decl "set" sets nil )
(group? const-decl "bool" group_def "algebra/" )
(one1 formal-const-decl "T1" isomorphism_theorems nil )
(* formal-const-decl "[T1, T1 -> T1]" isomorphism_theorems 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 isomorphism_theorems nil )
(restrict const-decl "R" restrict nil )
(image const-decl "set[R]" function_image nil )
(extend const-decl "R" extend nil )
(FALSE const-decl "bool" booleans nil )
(subgroup_contain type-eq-decl nil groups_scaf nil )
(f!1 skolem-const-decl
"homomorphism[T1, *, one1, T2, o, one2](G!1, GP!1)"
isomorphism_theorems nil )
(GP!1 skolem-const-decl "group[T2, o, one2]" isomorphism_theorems
nil )
(kernel const-decl "subgroup[T1, *, one1](G)" homomorphisms
"algebra/" )
(subgroup type-eq-decl nil group "algebra/" )
(homomorphism type-eq-decl nil homomorphisms "algebra/" )
(homomorphism? const-decl "bool" homomorphisms "algebra/" )
(one2 formal-const-decl "T2" isomorphism_theorems nil )
(O formal-const-decl "[T2, T2 -> T2]" isomorphism_theorems nil )
(T2 formal-type-decl nil isomorphism_theorems nil )
(subset? const-decl "bool" sets nil )
(G!1 skolem-const-decl "group[T1, *, one1]" isomorphism_theorems
nil )
(subgroup? const-decl "bool" group_def "algebra/" )
(AND const-decl "[bool, bool -> bool]" booleans nil )
(group nonempty-type-eq-decl nil group "algebra/" )
(homo_inv_image_normal formula-decl nil homomorphism_lemmas nil )
(x!1 skolem-const-decl "T1" isomorphism_theorems nil )
(a!1 skolem-const-decl "(G!1)" isomorphism_theorems nil )
(h!2 skolem-const-decl "(N!1)" isomorphism_theorems nil )
(inv const-decl "{y | x * y = one AND y * x = one}" group
"algebra/" )
(* const-decl "set[T]" cosets "algebra/" )
(* const-decl "set[T]" cosets "algebra/" )
(product_in formula-decl nil group "algebra/" )
(inv_in formula-decl nil group "algebra/" )
(homo_image_normal formula-decl nil homomorphism_lemmas nil )
(normal_subgroup type-eq-decl nil normal_subgroups "algebra/" )
(normal_subgroup? const-decl "boolean" normal_subgroups "algebra/" )
(N!1 skolem-const-decl
"subgroup_contain[T1, *, one1](G!1, kernel(G!1, GP!1)(f!1))"
isomorphism_theorems nil )
(homo_image formula-decl nil homomorphism_lemmas nil )
(bijective? const-decl "bool" functions nil )
(surjective? const-decl "bool" functions nil )
(y!1 skolem-const-decl "subgroup[T2, o, one2](GP!1)"
isomorphism_theorems nil )
(x!2 skolem-const-decl "(G!1)" isomorphism_theorems nil )
(x!1 skolem-const-decl "T2" isomorphism_theorems nil )
(IF const-decl "[boolean, T, T -> T]" if_def nil )
(homo_inv_image formula-decl nil homomorphism_lemmas nil )
(kernel_in_inv_image formula-decl nil homomorphism_lemmas nil )
(subgroup_is_group formula-decl nil group "algebra/" )
(injective? const-decl "bool" functions nil )
(NOT const-decl "[bool -> bool]" booleans nil )
(homo_inv_image_image_cor formula-decl nil homomorphism_lemmas nil )
(inverse_image const-decl "set[D]" function_image nil )
(= const-decl "[T, T -> boolean]" equalities nil )
(x!1 skolem-const-decl "T1" isomorphism_theorems nil )
(member const-decl "bool" sets nil )
(subset_is_partial_order name-judgement "(partial_order?[set[T]])"
sets_lemmas nil )
(T2_is_group formula-decl nil isomorphism_theorems nil )
(T1_is_group formula-decl nil isomorphism_theorems nil ))
shostak)))
Messung V0.5 in Prozent C=100 H=100 G=100
¤ Dauer der Verarbeitung: 0.429 Sekunden
(vorverarbeitet am 2026-04-27)
¤
*© Formatika GbR, Deutschland