2013-09-03 10:44:51 -07:00
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Set: pp::colors
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Set: pp::unicode
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2013-08-31 19:15:48 -07:00
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Assumed: f
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Assumed: N
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Assumed: n1
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Assumed: n2
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2013-09-02 12:29:21 -07:00
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Set: lean::pp::implicit
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2013-12-21 17:02:16 -08:00
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@f N n1 n2
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@f ((N → N) → N → N) (λ x : N → N, x) (λ y : N → N, y)
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2013-08-31 19:15:48 -07:00
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Assumed: EqNice
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2013-12-21 17:02:16 -08:00
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@EqNice N n1 n2
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@f N n1 n2 : N
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2014-02-01 18:27:14 -08:00
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@congr : ∀ (A B : (Type U)) (f g : A → B) (a b : A), @eq (A → B) f g → @eq A a b → @eq B (f a) (g b)
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2013-12-21 17:02:16 -08:00
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@f N n1 n2
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2013-08-31 19:15:48 -07:00
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Assumed: a
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Assumed: b
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Assumed: c
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Assumed: g
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Assumed: H1
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Proved: Pr
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2014-01-05 12:05:08 -08:00
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axiom H1 : @eq N a b ∧ @eq N b c
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theorem Pr : @eq N (g a) (g c) :=
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2014-01-05 19:10:21 -08:00
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@congr N
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2014-01-16 15:07:51 -08:00
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N
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2013-12-21 17:02:16 -08:00
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g
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g
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a
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c
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2014-01-05 19:10:21 -08:00
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(@refl (N → N) g)
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2014-01-09 08:33:52 -08:00
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(@trans N a b c (@and_eliml (@eq N a b) (@eq N b c) H1) (@and_elimr (@eq N a b) (@eq N b c) H1))
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