(** The Drinker's paradox [[Smullyan78]] and its dual (a weak form of indefinite description, see e.g. in [[WarrenDienerMcKubreJordens18]])  [[Smullyan78]] What is the Name of this Book? Raymond Smullyan, 1978.  [[WarrenDienerMcKubreJordens18]] The Drinker Paradox and its Dual, Louis Warren and Hannes Diener and Maarten McKubre-Jordens, 2018, unpublished. *)
Definition DrinkerParadox A :=
forall (P:A -> Prop),
inhabited A -> exists x, P x -> forall y, P y.
Definition DualDrinkerParadox A :=
forall (P:A -> Prop),
inhabited A -> exists x, (exists x, P x) -> P x.
(** Independence of general premises is equivalent to the dual drinker's paradox *)

Lemma independence_general_premises_dual_drinker A :
IndependenceOfGeneralPremises A <-> DualDrinkerParadox A.