26 lines
833 B
Text
26 lines
833 B
Text
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Set: pp::colors
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Set: pp::unicode
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Assumed: a
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Assumed: P
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Assumed: f
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Assumed: g
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Assumed: H1
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Assumed: H2
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Assumed: H3
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Proved: T1
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Proved: T2
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Proved: T3
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Proved: T4
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Proved: T5
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Proved: T6
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Proved: T7
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Proved: T8
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Theorem T1 : ∃ x y : ℤ, P (f y x) (f y x) := ExistsIntro (g a) (ExistsIntro a H1)
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Theorem T2 : ∃ x : ℤ, P (f x (g x)) (f x (g x)) := ExistsIntro a H1
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Theorem T3 : ∃ x : ℤ, P (f x x) (f x x) := ExistsIntro (g a) H2
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Theorem T4 : ∃ x : ℤ, P (f (g a) x) (f x x) := ExistsIntro (g a) H2
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Theorem T5 : ∃ x : ℤ, P x x := ExistsIntro (f (g a) (g a)) H2
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Theorem T6 : ∃ x y : ℤ, P x y := ExistsIntro (f (g a) (g a)) (ExistsIntro (g a) H3)
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Theorem T7 : ∃ x : ℤ, P (f x x) x := ExistsIntro (g a) H3
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Theorem T8 : ∃ x y : ℤ, P (f x x) y := ExistsIntro (g a) (ExistsIntro (g a) H3)
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