proposition: Lemma Exists_nil_eq : forall P, Exists P nil = False.
proof: Proof. Proof using. intros. extens. iff M. { invert* M. } { false. } Qed.
imports: Coq.Classes.Morphisms TLC(LibTactics LibLogic LibReflect LibOperation LibProd LibOption LibNat LibInt LibWf LibMonoid LibRelation)