24 lines
979 B
Text
24 lines
979 B
Text
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Set: pp::colors
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Set: pp::unicode
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Assumed: C
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Assumed: D
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Assumed: R
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Proved: R2
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Set: lean::pp::implicit
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Variable C {A B : Type} (H : A = B) (a : A) : B
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Definition C::explicit (A B : Type) (H : A = B) (a : A) : B := C H a
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Variable D {A A' : Type} {B : A → Type} {B' : A' → Type} (H : (Π x : A, B x) = (Π x : A', B' x)) : A = A'
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Definition D::explicit (A A' : Type) (B : A → Type) (B' : A' → Type) (H : (Π x : A, B x) = (Π x : A', B' x)) : A =
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A' :=
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D H
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Variable R {A A' : Type} {B : A → Type} {B' : A' → Type} (H : (Π x : A, B x) = (Π x : A', B' x)) (a : A) :
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(B a) = (B' (C::explicit A A' (D::explicit A A' B B' H) a))
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Definition R::explicit (A A' : Type)
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(B : A → Type)
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(B' : A' → Type)
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(H : (Π x : A, B x) = (Π x : A', B' x))
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(a : A) : (B a) = (B' (C (D H) a)) :=
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R H a
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Theorem R2 (A1 A2 B1 B2 : Type) (H : A1 → B1 = A2 → B2) (a : A1) : B1 = B2 :=
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R::explicit A1 A2 (λ _ : A1, B1) (λ _ : A2, B2) H a
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