proposition: Lemma filter_app (T : Type) (F : set_system T) : Filter F -> forall P Q : set T, F (fun x => P x -> Q x) -> F P -> F Q.
proof: Proof. by move=> FF P Q subPQ FP; near=> x do suff: P x. Unshelve. all: by end_near. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed