30 lines
853 B
Text
30 lines
853 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::explicit N n1 n2
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f::explicit ((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::explicit N n1 n2
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N
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Π (A : Type U) (B : A → Type U) (f g : Π x : A, B x) (a b : A), (f = g) → (a = b) → ((f a) = (g b))
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f::explicit 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 : a = b ∧ b = c
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Theorem Pr : (g a) = (g c) :=
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let κ::1 := Trans::explicit
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N
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a
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b
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c
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(Conjunct1::explicit (a = b) (b = c) H1)
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(Conjunct2::explicit (a = b) (b = c) H1)
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in Congr::explicit N (λ x : N, N) g g a c (Refl::explicit (N → N) g) κ::1
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