(** * Continuous extension of Rsqrt on R *)
Definition sqrt (x:R) : R :=
  match Rcase_abs x with
    | left _ => 0
    | right a => Rsqrt (mknonnegreal x (Rge_le _ _ a))
  end.

Lemma sqrt_less : forall x:R, 0 <= x -> 1 < x -> sqrt x < x.