proposition: Lemma all_decomp_neq0 (A : set rT) : A !=set0 -> (forall X, decomp A X -> X !=set0).
proof: Proof. move=> /set0P AN0; rewrite /decomp/= (negPf AN0). case: pselect => //= Am; first by case: cid => //= ? []. by move=> X ->; exact/set0P. 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)