proposition: Lemma filter_prod1 {T U} {F : set_system T} {G : set_system U} {FG : Filter G} (P : set T) : (\forall x \near F, P x) -> \forall x \near F & _ \near G, P x.
proof: Proof. move=> FP; exists (P, setT)=> //= [|[?? []//]]. by split=> //; apply: filterT. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed