32 lines
773 B
Text
32 lines
773 B
Text
Set: pp::colors
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Set: pp::unicode
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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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Set: lean::pp::implicit
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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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Assumed: EqNice
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@EqNice N n1 n2
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@f N n1 n2 : N
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@congr :
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∀ (A : TypeU) (B : A → TypeU) (f g : ∀ x : A, B x) (a b : A),
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@eq (∀ x : A, B x) f g → @eq A a b → f a == g b
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@f N n1 n2
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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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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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@congr N
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(λ x : N, N)
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g
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g
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a
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c
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(@refl (N → N) g)
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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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