Set: pp::colors
  Set: pp::unicode
  Assumed: N
  Assumed: a
  Assumed: b
  Assumed: c
  Assumed: P
  Assumed: H3
  Proved: T1
  Proved: T2
  Proved: T3
  Proved: T4
theorem T1 : ∃ x y z : N, P x y z :=
    @exists_intro
        N
        (λ x : N, ∃ y z : N, P x y z)
        a
        (@exists_intro N (λ y : N, ∃ z : N, P a y z) b (@exists_intro N (λ z : N, P a b z) c H3))
theorem T2 : ∃ x y z : N, P x y z := exists_intro a (exists_intro b (exists_intro c H3))
theorem T3 : ∃ x y z : N, P x y z := exists_intro a (exists_intro b (exists_intro c H3))
theorem T4 (H : P a a b) : ∃ x y z : N, P x y z := exists_intro a (exists_intro a (exists_intro b H))