proposition: Lemma filterP_strong T (F : set_system T) {FF : Filter F} (P : set T) : (exists Q : set T, exists FQ : F Q, forall x : T, Q x -> P x) <-> F P.
proof: Proof. split; last by exists P. by move=> [Q [FQ QP]]; apply: (filterS QP). Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed