proposition: Lemma edist_lt_ball r (xy : X * X) : (edist xy < r%:E)%E -> ball xy.1 r xy.2.
proof: Proof. case/ereal_inf_lt => ? [+ []] => _/posnumP[eps] bxye <-; rewrite lte_fin. by move/ltW/le_ball; exact. 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