proposition: Lemma cvg_at_rightE (R : numFieldType) (V : normedModType R) (f : R -> V) x : cvg (f @ x^') -> lim (f @ x^') = lim (f @ x^'+).
proof: Proof. move=> cvfx; apply/Logic.eq_sym. apply: (@cvg_lim _ _ _ (at_right _)) => // A /cvfx /nbhs_ballP [_ /posnumP[e] xe_A]. by exists e%:num => //= y xe_y; rewrite lt_def => /andP [xney _]; apply: xe_A. 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