proposition: Lemma cover_decomp (A : set rT) : \bigcup_(X in decomp A) X = A.
proof: Proof. rewrite /decomp; case: ifP => [/eqP->|_]; first by rewrite bigcup0. case: pselect => // Am; first by case: cid => //= ? []. by rewrite bigcup_set1. 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)