proposition: Lemma forall_inPn D P : reflect (exists2 x, x \in D & ~~ P x) (~~ [forall x in D, P x]).
proof: Proof. rewrite negb_forall_in. exact: exists_inP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)