proposition: Lemma filter_prod2 {T U} {F : set_system T} {G : set_system U} {FF : Filter F} (P : set U) : (\forall y \near G, P y) -> \forall _ \near F & y \near G, P y.
proof: Proof. move=> FP; exists (setT, P)=> //= [|[?? []//]]. 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