18 lines
No EOL
831 B
Text
18 lines
No EOL
831 B
Text
import Int.
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variable a : Int
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variable P : Int -> Int -> Bool
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variable f : Int -> Int -> Int
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variable g : Int -> Int
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axiom H1 : P (f a (g a)) (f a (g a))
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axiom H2 : P (f (g a) (g a)) (f (g a) (g a))
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axiom H3 : P (f (g a) (g a)) (g a)
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theorem T1 : exists x y : Int, P (f y x) (f y x) := exists_intro _ (exists_intro _ H1)
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theorem T2 : exists x : Int, P (f x (g x)) (f x (g x)) := exists_intro _ H1
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theorem T3 : exists x : Int, P (f x x) (f x x) := exists_intro _ H2
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theorem T4 : exists x : Int, P (f (g a) x) (f x x) := exists_intro _ H2
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theorem T5 : exists x : Int, P x x := exists_intro _ H2
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theorem T6 : exists x y : Int, P x y := exists_intro _ (exists_intro _ H3)
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theorem T7 : exists x : Int, P (f x x) x := exists_intro _ H3
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theorem T8 : exists x y : Int, P (f x x) y := exists_intro _ (exists_intro _ H3)
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print environment 8. |