21 lines
674 B
Text
21 lines
674 B
Text
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))
|