proposition: Lemma negb_exists P : ~~ [exists x, P x] = [forall x, ~~ P x].
proof: Proof. by apply/negbLR/esym/eq_existsb=> x; apply: negbK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)