(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Local Open Scope R_scope.
(* begin hide *)
Notation Rmin_pos := Rmin_pos (only parsing). (* compat *)
(* end hide *)
(* begin hide *)
Notation Rmin_2 := Rmin_glb_lt (only parsing).
(* end hide *)

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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).