apply CV_mult.
- intros eps ep; exists 0%nat; rewrite Rdist_eq; intros n _; assumption.
- exact (cv_infty_cv_0 pow_2_n pow_2_n_infty).
Qed.

(* Specifications: *)
(** Intermediate Value Theorem *)
Lemma IVT :
forall (f:R -> R) (x y:R),
continuity f ->
x < y -> f x < 0 -> 0 < f y -> { z:R | x <= z <= y /\ f z = 0 }.
Lemma IVT_cor :
forall (f:R -> R) (x y:R),
continuity f ->
x <= y -> f x * f y <= 0 -> { z:R | x <= z <= y /\ f z = 0 }.
(** We can now define the square root function as the reciprocal transformation of the square function *)
Lemma Rsqrt_exists :
forall y:R, 0 <= y -> { z:R | 0 <= z /\ y = Rsqr z }.