proposition: Lemma ncvg_uniq u l1 l2 : ncvg u l1 -> ncvg u l2 -> l1 = l2.
proof: Proof. move=> cv1 cv2; apply/eqP; case: (l1 =P l2) => // /eqP. case/separable=> [n1] [n2] h; move: (cv1 n1) (cv2 n2). case=> [K1 c1] [K2 c2]; pose K := maxn K1 K2. move/(_ (u K)): h; rewrite !inE/= !(c1, c2) //. by apply/leq_maxl. by apply/leq_maxr. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.bigenough.bigenough mathcomp.classical(boolp classical_sets functions) mathcomp.classical(mathcomp_extra) xfinmap ereal reals discrete topology