21 lines
676 B
Text
21 lines
676 B
Text
Set: pp::colors
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Set: pp::unicode
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Assumed: N
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Assumed: a
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Assumed: b
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Assumed: c
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Assumed: P
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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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Theorem T1 : ∃ x y z : N, P x y z :=
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@ExistsIntro
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N
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(λ x : N, ∃ y z : N, P x y z)
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a
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(@ExistsIntro N (λ x : N, ¬ (∀ x::1 : N, ¬ P a x x::1)) b (@ExistsIntro N (λ z : N, P a b z) c H3))
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Theorem T2 : ∃ x y z : N, P x y z := ExistsIntro a (ExistsIntro b (ExistsIntro c H3))
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Theorem T3 : ∃ x y z : N, P x y z := ExistsIntro a (ExistsIntro b (ExistsIntro c H3))
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Theorem T4 (H : P a a b) : ∃ x y z : N, P x y z := ExistsIntro a (ExistsIntro a (ExistsIntro b H))
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