2022-07-26 07:57:44 +02:00
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let transport : Π (A : Type) Π (f : A → Type) Π (x : A) Π (y : A)
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Id A x y → f x → f y
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≔ λA.λf.λx.λy. J A x y (λa.λb.λ_. f a → f b) (λa.a)
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let ap : Π (A : Type) Π (B : Type) Π (f : A → B)
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Π (x : A) Π (y : A) Id A x y → Id B (f x) (f y)
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≔ λA.λB.λf.λx.λy. J A x y (λa.λb.λ_. Id B (f a) (f b)) (refl B (f x))
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2022-07-28 15:46:00 +02:00
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let cat : Π (A : Type) Π (x : A) Π (y : A) Π (z : A)
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Id A x y → Id A y z → Id A x z
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≔ λA.λx.λy.λz.λp.λq. J A y z (λa.λb.λr. Id A x b) (refl A y) q
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