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::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
f::explicit N n1 n2 : N
Congr::explicit :
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
f::explicit N n1 n2
Assumed: a
Assumed: b
Assumed: c
Assumed: g
Assumed: H1
Proved: Pr
Axiom H1 : eq::explicit N a b ∧ eq::explicit N b c
Theorem Pr : eq::explicit N (g a) (g c) :=
Congr::explicit
N
(λ x : N, N)
g
g
a
c
(Refl::explicit (N → N) g)
(Trans::explicit
N
a
b
c
(Conjunct1::explicit (eq::explicit N a b) (eq::explicit N b c) H1)
(Conjunct2::explicit (eq::explicit N a b) (eq::explicit N b c) H1))