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 : ∀ (A B : TypeU) (f g : A → B) (a b : A), @eq (A → B) f g → @eq A a b → @eq 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
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))