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refactor(library/theories/group_theory/hom): cleanup definition

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Leonardo de Moura 2015-10-22 18:13:29 -07:00
parent 21501ccfa4
commit 33006919b3
1 changed files with 1 additions and 4 deletions
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library/theories/group_theory/hom.lean
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@ -116,10 +116,8 @@ variable {H : set A}
variable [is_subgH : is_subgroup H]
include is_subgH
section mem_reducible
local attribute mem [reducible]
theorem hom_map_subgroup : is_subgroup (f '[H]) :=
have Pone : 1 ∈ f '[H], from mem_image subg_has_one (hom_map_one f),
have Pone : 1 ∈ f '[H], from mem_image (@subg_has_one _ _ H _) (hom_map_one f),
have Pclosed : mul_closed_on (f '[H]), from hom_map_mul_closed f H subg_mul_closed,
assert Pinv : ∀ b, b ∈ f '[H] → b⁻¹ ∈ f '[H], from
assume b, assume Pimg,
@ -128,7 +126,6 @@ theorem hom_map_subgroup : is_subgroup (f '[H]) :=
assert Pfainv : (f a)⁻¹ ∈ f '[H], from mem_image Painv (hom_map_inv f a),
and.right Pa ▸ Pfainv,
is_subgroup.mk Pone Pclosed Pinv
end mem_reducible
end
section hom_theorem