proposition: Lemma filter_ex_subproof {T : Type} (F : set_system T) : ~ F set0 -> (forall P, F P -> exists x, P x).
proof: Proof. move=> NFset0 P FP; apply: contra_notP NFset0 => nex; suff <- : P = set0 by []. by rewrite funeqE => x; rewrite propeqE; split=> // Px; apply: nex; exists x. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed