proposition: Lemma normm_lt_split (x y : V) (e : R) : `|x| < e / 2 -> `|y| < e / 2 -> `|x + y| < e.
proof: Proof. by move=> xlt ylt; rewrite -[y]opprK (@distm_lt_split 0) ?subr0 ?opprK ?add0r. 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