(* begin hide *)
Notation Rmin_2 := Rmin_glb_lt (only parsing).
(* end hide *)

(**********)
Lemma continuous_neq_0 :
forall (f:R -> R) (x0:R),
continuity_pt f x0 ->
f x0 <> 0 ->
exists eps : posreal, (forall h:R, Rabs h < eps -> f (x0 + h) <> 0).