Created
May 2, 2024 06:28
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universe u | |
inductive Eq' {A : Type u} : A → A → Type u | |
| idp (a : A) : Eq' a a | |
def f {A : Type u} {a b : A} : Eq' a b → Eq a b := | |
λ q => @Eq'.casesOn A a (λ b q' => Eq a b) b q (Eq.refl a) | |
def g {A : Type u} {a b : A} : Eq a b → Eq' a b := | |
λ p => @Eq.casesOn A a (λ b p' => Eq' a b) b p (Eq'.idp a) | |
def fg {A : Type u} {a b : A} (p : Eq a b) : f (g p) = p := | |
rfl | |
def gf {A : Type u} {a b : A} (q : Eq' a b) : g (f q) = q := | |
@Eq'.casesOn A a (λ b q' => g (f q') = q') b q rfl |
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