29 lines
1,003 B
Text
29 lines
1,003 B
Text
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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 option: lean::pp::implicit
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f::explicit N n1 n2
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f::explicit ((N [33m→[0m N) [33m→[0m N [33m→[0m N) ([33mλ[0m x : N [33m→[0m N, x) ([33mλ[0m y : N [33m→[0m 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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[33mΠ[0m (A : [36mType[0m u) (B : A [33m→[0m [36mType[0m u) (f g : [33mΠ[0m x : A, B x) (a b : A) (H1 : f = g) (H2 : 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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[34mAxiom[0m H1 : a = b ∧ b = c
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[34mTheorem[0m Pr : (g a) = (g c) [33m:=[0m
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[33mlet[0m κ::1 [33m:=[0m 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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[33min[0m Congr::explicit N ([33mλ[0m x : N, N) g g a c (Refl::explicit (N [33m→[0m N) g) κ::1
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