proposition: Lemma ball_open (R : numDomainType) (V : normedModType R) (x : V) (r : R) : 0 < r -> open (ball x r).
proof: Proof. rewrite openE -ball_normE /interior => r0 y /= Bxy; near=> z. rewrite /= (le_lt_trans (ler_distD y _ _)) // addrC -ltrBrDr. by near: z; apply: cvgr_dist_lt; rewrite // subr_gt0. Unshelve. all: by end_near. 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