proposition: Lemma filter_not_empty_ex {T : Type} (F : set_system T) : (forall P, F P -> exists x, P x) -> ~ F set0.
proof: Proof. by move=> /(_ set0) ex /ex []. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed