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kim-emmergify[bot]
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chore(category_theory/isomorphism): use @[simps] (#2181)
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
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src/category_theory/isomorphism.lean

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@@ -86,24 +86,19 @@ by cases α; refl
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⟨λ h, symm_symm_eq α ▸ symm_symm_eq β ▸ congr_arg symm h, congr_arg symm⟩
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/-- Identity isomorphism. -/
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@[refl] def refl (X : C) : X ≅ X :=
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@[refl, simps] def refl (X : C) : X ≅ X :=
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{ hom := 𝟙 X,
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inv := 𝟙 X }
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@[simp] lemma refl_hom (X : C) : (iso.refl X).hom = 𝟙 X := rfl
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@[simp] lemma refl_inv (X : C) : (iso.refl X).inv = 𝟙 X := rfl
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@[simp] lemma refl_symm (X : C) : (iso.refl X).symm = iso.refl X := rfl
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/-- Composition of two isomorphisms -/
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@[trans] def trans (α : X ≅ Y) (β : Y ≅ Z) : X ≅ Z :=
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@[trans, simps] def trans (α : X ≅ Y) (β : Y ≅ Z) : X ≅ Z :=
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{ hom := α.hom ≫ β.hom,
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inv := β.inv ≫ α.inv }
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infixr ` ≪≫ `:80 := iso.trans -- type as `\ll \gg`.
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@[simp] lemma trans_hom (α : X ≅ Y) (β : Y ≅ Z) : (α ≪≫ β).hom = α.hom ≫ β.hom := rfl
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@[simp] lemma trans_inv (α : X ≅ Y) (β : Y ≅ Z) : (α ≪≫ β).inv = β.inv ≫ α.inv := rfl
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@[simp] lemma trans_mk {X Y Z : C}
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(hom : X ⟶ Y) (inv : Y ⟶ X) (hom_inv_id) (inv_hom_id)
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(hom' : Y ⟶ Z) (inv' : Z ⟶ Y) (hom_inv_id') (inv_hom_id') (hom_inv_id'') (inv_hom_id'') :

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