lean2/tests/lean/exists2.lean.expected.out

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Set: pp::colors
Set: pp::unicode
Imported 'Int'
Assumed: a
Assumed: P
Assumed: f
Assumed: g
Assumed: H1
Assumed: H2
Assumed: H3
Proved: T1
Proved: T2
Proved: T3
Proved: T4
Proved: T5
Proved: T6
Proved: T7
Proved: T8
Theorem T1 : ∃ x y : , P (f y x) (f y x) := ExistsIntro (g a) (ExistsIntro a H1)
Theorem T2 : ∃ x : , P (f x (g x)) (f x (g x)) := ExistsIntro a H1
Theorem T3 : ∃ x : , P (f x x) (f x x) := ExistsIntro (g a) H2
Theorem T4 : ∃ x : , P (f (g a) x) (f x x) := ExistsIntro (g a) H2
Theorem T5 : ∃ x : , P x x := ExistsIntro (f (g a) (g a)) H2
Theorem T6 : ∃ x y : , P x y := ExistsIntro (f (g a) (g a)) (ExistsIntro (g a) H3)
Theorem T7 : ∃ x : , P (f x x) x := ExistsIntro (g a) H3
Theorem T8 : ∃ x y : , P (f x x) y := ExistsIntro (g a) (ExistsIntro (g a) H3)