2013-09-09 05:54:22 +00:00
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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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2014-01-05 20:05:08 +00:00
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import "kernel"
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import "Nat"
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variable C {A B : Type} (H : @eq Type A B) (a : A) : B
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variable D {A A' : Type} {B : A → Type} {B' : A' → Type} (H : @eq Type (Π x : A, B x) (Π x : A', B' x)) :
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2013-12-22 01:02:16 +00:00
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@eq Type A A'
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2014-01-05 20:05:08 +00:00
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variable R {A A' : Type} {B : A → Type} {B' : A' → Type} (H : @eq Type (Π x : A, B x) (Π x : A', B' x)) (a : A) :
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2013-12-22 01:02:16 +00:00
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@eq Type (B a) (B' (@C A A' (@D A A' (λ x : A, B x) (λ x : A', B' x) H) a))
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2014-01-05 20:05:08 +00:00
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theorem R2 (A1 A2 B1 B2 : Type) (H : @eq Type (A1 → B1) (A2 → B2)) (a : A1) : @eq Type B1 B2 :=
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2013-12-22 01:02:16 +00:00
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@R A1 A2 (λ x : A1, B1) (λ x : A2, B2) H a
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