24 lines
742 B
Text
24 lines
742 B
Text
module
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structure Cat (C : Type) where
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hom : C → C → Type
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comp {x y z : C} (f : hom x y) (g : hom y z) : hom x z
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id x : hom x x
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structure Foo {C D : Type} (ℭ₁ : Cat C) (ℭ₂ : Cat D) where
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obj : C → D
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variable {C D : Type} {ℭ₁ : Cat C} {ℭ₂ : Cat D}
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structure Iso (x y : C) where
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hom : ℭ₁.hom x y
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inv : ℭ₁.hom y x
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hom_inv_id : ℭ₁.comp hom inv = ℭ₁.id _
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inv_hom_id : ℭ₁.comp hom inv = ℭ₁.id _
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attribute [grind =] Iso.hom_inv_id Iso.inv_hom_id
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#guard_msgs in -- Should not produce any issues
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set_option trace.grind.issues true in
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example (F G : Foo ℭ₁ ℭ₂) (e : ∀ (x : C), Iso (F.obj x) (G.obj x)) (x : C) :
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ℭ₂.comp (e x).hom (e x).inv = ℭ₂.id _ := by
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grind
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