lean2/tests/lean/tst4.lean.expected.out

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Set: pp::colors
Set: pp::unicode
Assumed: f
Assumed: N
Assumed: n1
Assumed: n2
Set: lean::pp::implicit
@f N n1 n2
@f ((N → N) → N → N) (λ x : N → N, x) (λ y : N → N, y)
Assumed: EqNice
@EqNice N n1 n2
@f N n1 n2 : N
@congr : Π (A : TypeU) (B : A → TypeU) (f g : Π x : A, B x) (a b : A), f == g → a == b → f a == g b
@f N n1 n2
Assumed: a
Assumed: b
Assumed: c
Assumed: g
Assumed: H1
Proved: Pr
axiom H1 : @eq N a b ∧ @eq N b c
theorem Pr : @eq N (g a) (g c) :=
@congr N
(λ x : N, N)
g
g
a
c
(@refl (N → N) g)
(@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))