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

  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))