proposition: Lemma interior_bigcup I (D : set I) (f : I -> set T) : \bigcup_(i in D) (f i)^° `<=` (\bigcup_(i in D) f i)^°.
proof: Proof. move=> p [i Di]; rewrite /interior nbhsE => - [B [Bop Bp] sBfi]. by exists B => // ? /sBfi; exists i. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed