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February 12, 2020 11:05
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Drinker paradox
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Require Import Classical. | |
From mathcomp Require Import all_ssreflect. | |
Section Drinker. | |
Variable P : Type. | |
Variable p : P. | |
Variable D : P -> Prop. | |
Theorem drinker : exists (x : P), D x -> forall y, D y. | |
Proof. | |
case (classic (exists x, ~ D x)) => [ [ x H ] | H ]. | |
- by exists x => /H. | |
- exists p => ? x. | |
case (classic (D x)) => // ?. | |
case H. by exists x. | |
Qed. | |
End Drinker. |
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