proposition: Lemma bigcup_open (I : Type) (D : set I) (f : I -> set T) : (forall i, D i -> open (f i)) -> open (\bigcup_(i in D) f i).
proof: Proof. rewrite openE => fop p [i Di]. by have /fop fiop := Di; move/fiop; apply: filterS => ??; 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