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

Assumed: f
Assumed: N
Assumed: n1
Assumed: n2
Set option: lean::pp::implicit
f::explicit N n1 n2
f::explicit ((N → N) → N → N) (λ x : N → N, x) (λ y : N → N, y)
Assumed: EqNice
EqNice::explicit N n1 n2
N
Π (A : Type u) (B : A → Type u) (f g : Π x : A, B x) (a b : A) (H1 : f = g) (H2 : a = b), (f a) = (g b)
f::explicit N n1 n2
Assumed: a
Assumed: b
Assumed: c
Assumed: g
Assumed: H1
Proved: Pr
Axiom H1 : a = b ∧ b = c
Theorem Pr : (g a) = (g c) :=
let κ::1 := Trans::explicit
N
a
b
c
(Conjunct1::explicit (a = b) (b = c) H1)
(Conjunct2::explicit (a = b) (b = c) H1)
in Congr::explicit N (λ x : N, N) g g a c (Refl::explicit (N → N) g) κ::1