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(*         *      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)         *)
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Local Open Scope R_scope.
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(** Rsqr : some results                             *)
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Ltac ring_Rsqr := unfold Rsqr; ring.

Lemma triangle_rectangle :
forall x y z:R,
0 <= z -> Rsqr x + Rsqr y <= Rsqr z -> - z <= x <= z /\ - z <= y <= z.