stuff
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1 changed files with 20 additions and 7 deletions
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@ -113,13 +113,26 @@ parameters {A B C : AbGroup} (ses : SES A B C)
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local abbreviation q := ab_qg_map (kernel_subgroup g)
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local abbreviation q := ab_qg_map (kernel_subgroup g)
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local abbreviation B_mod_A := quotient_ab_group (kernel_subgroup g)
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local abbreviation B_mod_A := quotient_ab_group (kernel_subgroup g)
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--definition quotient_SES {A B C : AbGroup} (ses : SES A B C) :
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definition SES_of_triangle_left {A' : AbGroup} (α : A' ≃g A) (f' : A' →g B) (H : Π a' : A', f (α a') = f' a') : SES A' B C :=
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-- quotient_ab_group (image_subgroup (SES.f ses)) ≃g C :=
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begin
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-- begin
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fapply SES.mk,
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-- fapply ab_group_first_iso_thm B C (SES.g ses),
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exact f',
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-- end
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exact g,
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fapply is_embedding_of_is_injective,
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-- definition pre_right_extend_SES (to separate the following definition and replace C with B/A)
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intro x y p,
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fapply eq_of_fn_eq_fn (equiv_of_isomorphism α),
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fapply @is_injective_of_is_embedding _ _ f (SES.Hf ses) (α x) (α y),
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rewrite [H x], rewrite [H y], exact p,
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exact SES.Hg ses,
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fapply is_exact.mk,
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intro a',
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rewrite [(H a')⁻¹],
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fapply is_exact.im_in_ker (SES.ex ses),
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intro b p,
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have t : trunctype.carrier (subgroup_to_rel (image_subgroup f) b), from is_exact.ker_in_im (SES.ex ses) b p,
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induction t, fapply tr, induction a with a q, fapply fiber.mk, exact α⁻¹ᵍ a, rewrite [(H (α⁻¹ᵍ a))⁻¹],
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krewrite [right_inv (equiv_of_isomorphism α) a], assumption
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end
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definition quotient_codomain_SES : B_mod_A ≃g C :=
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definition quotient_codomain_SES : B_mod_A ≃g C :=
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begin
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begin
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