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 :=
@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))