proposition: Lemma cvgr_neq0 {T} {F : set_system T} {FF : Filter F} (f : T -> V) (y : V) : f @ F --> y -> y != 0 -> \forall t \near F, f t != 0.
proof: Proof. move=> Fy z; near do rewrite -normr_gt0. by apply: (@cvgr_norm_gt _ _ _ _ y); rewrite // normr_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