33 lines
790 B
Text
33 lines
790 B
Text
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import algebra.group data.set
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namespace group_hom
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open algebra
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-- ⁻¹ in eq.ops conflicts with group ⁻¹
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-- open eq.ops
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open set
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open function
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local attribute set [reducible]
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structure is_subgroup [class] {A : Type} (H : set A) : Type
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section
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variables {A B : Type}
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variable [s1 : group A]
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variable [s2 : group B]
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include s1
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include s2
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definition is_hom (f : A → B) := ∀ a b, f (a*b) = (f a)*(f b)
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variable f : A → B
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variable Hom : is_hom f
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definition ker : set A := λ a, (f a) = 1
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lemma ker.has_one (Hom : is_hom f) : 1 ∈ ker f := sorry
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theorem hom_map_one : f 1 = 1 := sorry
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theorem hom_map_mul_closed (Hom : is_hom f) (H : set A) : unit :=
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sorry
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variable {H : set A}
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variable [is_subgH : is_subgroup H]
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include is_subgH
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end
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end group_hom
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