lean2/tests/lean/exists2.lean.expected.out
Leonardo de Moura 7726ccad28 chore(builtin): rename nat, int and real modules to Nat, Int and Real.
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-01-01 13:52:25 -08:00

26 lines
850 B
Text
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

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)