(* Definition of the square root: R+->R *)
Definition Rsqrt (y:nonnegreal) : R :=
  let (a,_) := Rsqrt_exists (nonneg y) (cond_nonneg y) in a.

(* Specifications: *)
Lemma Rsqrt_positivity : forall x:nonnegreal, 0 <= Rsqrt x.
Lemma Rsqrt_Rsqrt : forall x:nonnegreal, Rsqrt x * Rsqrt x = x.