proposition: Lemma decomp_sub (A : set rT) (X : set T) : X \in decomp A -> X `<=` A.
proof: Proof. rewrite /decomp; case: ifP => _; first by rewrite inE/= => ->//. case: pselect => //= Am; last by rewrite inE => ->. by case: cid => //= D [_ _ _ _ ->] /[!inE] XD; apply: bigcup_sup. Qed.
imports: mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality fsbigop ) reals ereal signed topology normedtype sequences esum numfun HB(structures)