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 :=
|
|
@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))
|