18 lines
No EOL
819 B
Text
18 lines
No EOL
819 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) := ExistsIntro _ (ExistsIntro _ H1)
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Theorem T2 : exists x : Int, P (f x (g x)) (f x (g x)) := ExistsIntro _ H1
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Theorem T3 : exists x : Int, P (f x x) (f x x) := ExistsIntro _ H2
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Theorem T4 : exists x : Int, P (f (g a) x) (f x x) := ExistsIntro _ H2
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Theorem T5 : exists x : Int, P x x := ExistsIntro _ H2
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Theorem T6 : exists x y : Int, P x y := ExistsIntro _ (ExistsIntro _ H3)
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Theorem T7 : exists x : Int, P (f x x) x := ExistsIntro _ H3
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Theorem T8 : exists x y : Int, P (f x x) y := ExistsIntro _ (ExistsIntro _ H3)
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Show Environment 8. |