proposition: Lemma tuto_negb_exists : ~~ [exists x, P x] = [forall x, ~~ P x].
proof: Proof. rewrite negbK; congr (_ == 0); apply: eq_card => x. by rewrite !inE /= negbK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finset)