(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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.
(** * 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_Rsqr : forall x:R, 0 <= x -> sqrt (Rsqr x) = x.