proposition: Lemma is_cvgeM f g : lim (f @ F) *? lim (g @ F) -> cvg (f @ F) -> cvg (g @ F) -> cvg (f \* g @ F).
proof: Proof. by move=> fg fc gc; have /(_ _)/cvgP := cvgeM fg fc gc. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule