proposition: Lemma closed_bigI {I} (D : set I) (f : I -> set T) : (forall i, D i -> closed (f i)) -> closed (\bigcap_(i in D) f i).
proof: Proof. move=> fcl t clft i Di; have /fcl := Di; apply. by move=> A /clft [s [/(_ i Di)]]; exists s. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed