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Mathlib/Algebra/Category/ModuleCat/Subobject.lean

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@@ -45,9 +45,7 @@ noncomputable def subobjectModule : Subobject M ≃o Submodule R M :=
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· apply LinearEquiv.toModuleIso'Left
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apply LinearEquiv.ofBijective (LinearMap.codRestrict (LinearMap.range S.arrow) S.arrow _)
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constructor
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· simp only [← LinearMap.ker_eq_bot, LinearMap.mem_range, exists_apply_eq_apply,
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forall_const, LinearMap.ker_codRestrict]
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rw [ker_eq_bot_of_mono]
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· simpa [← LinearMap.ker_eq_bot, LinearMap.ker_codRestrict] using ker_eq_bot_of_mono ..
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· rw [← LinearMap.range_eq_top, LinearMap.range_codRestrict, Submodule.comap_subtype_self]
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exact LinearMap.mem_range_self _
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· apply LinearMap.ext

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