proposition: Lemma ncvg_homo_le (u : nat -> R) (l : \bar R) : (forall m n, (m <= n)%N -> u m <= u n) -> ncvg u l -> forall n, ((u n)%:E <= l)%E.
proof: Proof. move=> homo_u cvu n; rewrite leNgt. by apply/negP => /ncvg_homo_lt /(_ cvu) -/(_ homo_u n); rewrite ltxx. 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