proposition: Lemma exists_inPnn {T : finType} {D P : pred T} : reflect (forall x : T, x \in D -> P x) (~~ [exists x in D, ~~ P x]).
proof: Proof. rewrite negb_exists_in; under eq_forallb => ? do rewrite negbK. exact: forall_inP. Qed.
imports: Coq(Setoid Morphisms) mathcomp(all_ssreflect) GraphTheory(edone)