(** * 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_mult_alt : forall x y : R, 0 <= x -> sqrt (x * y) = sqrt x * sqrt y.