lean2/tests/lean/exists4.lean.expected.out

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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 :=
@ExistsIntro
N
(λ x : N, ∃ y z : N, P x y z)
a
(@ExistsIntro N (λ x : N, ¬ ∀ x::1 : N, ¬ P a x x::1) b (@ExistsIntro N (λ z : N, P a b z) c H3))
Theorem T2 : ∃ x y z : N, P x y z := ExistsIntro a (ExistsIntro b (ExistsIntro c H3))
Theorem T3 : ∃ x y z : N, P x y z := ExistsIntro a (ExistsIntro b (ExistsIntro c H3))
Theorem T4 (H : P a a b) : ∃ x y z : N, P x y z := ExistsIntro a (ExistsIntro a (ExistsIntro b H))