proposition: Lemma open_subspace_out (U : set (subspace A)) : U `<=` ~` A -> open U.
proof: Proof. move=> Usub; rewrite (_ : U = \bigcup_(i in U) [set i]). by apply: bigcup_open => ? ?; apply: open_subspace1out; exact: Usub. by rewrite eqEsubset; split => x; [move=> ?; exists x|case=> 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