16 lines
678 B
Text
16 lines
678 B
Text
|
Variable N : Type
|
||
|
|
Variables a b c : N
|
||
|
|
Variables P : N -> N -> N -> Bool
|
||
|
|
Axiom H3 : P a b c
|
||
|
|
|
||
|
|
Theorem T1 : exists x y z : N, P x y z := ExistsIntro::explicit N (fun x : N, exists y z : N, P x y z) a
|
||
|
|
(ExistsIntro::explicit N _ b
|
||
|
|
(ExistsIntro::explicit N (fun z : N, P a b z) c H3))
|
||
|
|
|
||
|
|
Theorem T2 : exists x y z : N, P x y z := ExistsIntro a (ExistsIntro b (ExistsIntro c H3))
|
||
|
|
|
||
|
|
Theorem T3 : exists x y z : N, P x y z := ExistsIntro _ (ExistsIntro _ (ExistsIntro _ H3))
|
||
|
|
|
||
|
|
Theorem T4 (H : P a a b) : exists x y z, P x y z := ExistsIntro _ (ExistsIntro _ (ExistsIntro _ H))
|
||
|
|
|
||
|
|
Show Environment 4
|