proposition: Lemma normm_leW (x : V) (e : R) : e > 0 -> `|x| <= e / 2 -> `|x| < e.
proof: Proof. by move=> /posnumP[{}e] /le_lt_trans ->//; rewrite [ltRHS]splitr ltr_pwDl. 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