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This commit is contained in:
Steve Awodey 2017-01-26 14:58:19 -05:00
parent 00e01fd2a6
commit c09f568992
1 changed files with 3 additions and 1 deletions
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4
algebra/quotient_group.hlean
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@ -247,6 +247,7 @@ namespace group
------------------------------------------------ ------------------------------------------------
-- FIRST ISOMORPHISM THEOREM -- FIRST ISOMORPHISM THEOREM
------------------------------------------------
definition kernel_quotient_extension {A B : AbGroup} (f : A →g B) : quotient_ab_group (kernel_subgroup f) →g B := definition kernel_quotient_extension {A B : AbGroup} (f : A →g B) : quotient_ab_group (kernel_subgroup f) →g B :=
@ -371,7 +372,8 @@ definition is_embedding_kernel_quotient_to_image {A B : AbGroup} (f : A →g B)
exact is_embedding_kernel_quotient_extension f exact is_embedding_kernel_quotient_extension f
end end
definition ab_group_first_iso_thm (A B : AbGroup) (f : A →g B) : quotient_ab_group (kernel_subgroup f) ≃g ab_image f := definition ab_group_first_iso_thm (A B : AbGroup) (f : A →g B)
: quotient_ab_group (kernel_subgroup f) ≃g ab_image f :=
begin begin
fapply isomorphism.mk, fapply isomorphism.mk,
exact ab_group_kernel_quotient_to_image f, exact ab_group_kernel_quotient_to_image f,