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(*  This file is part of WP plug-in of Frama-C.                           *)
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(*  Copyright (C) 2007-2018                                               *)
(*    CEA (Commissariat a l'energie atomique et aux energies              *)
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(* This file is generated by Why3's Coq-realize driver *)
(* Beware! Only edit allowed sections below    *)
Require Import BuiltIn.
Require Reals.R_sqrt.
Require BuiltIn.
Require real.Real.
Require real.RealInfix.
Require real.Square.

(* Why3 goal *)
Lemma sqrt_lin1 : forall (x:R), (1%R < x)%R -> ((Reals.R_sqrt.sqrt x) < x)%R.
Proof.
  intros x h1.
  refine (Reals.R_sqrt.sqrt_less _ _ h1).
  apply (Rle_trans 0 1 x Rle_0_1)%R.
  exact (Rlt_le _ _ h1).
Qed.

(* Why3 goal *)
Lemma sqrt_lin0 : forall (x:R), ((0%R < x)%R /\ (x < 1%R)%R) ->
  (x < (Reals.R_sqrt.sqrt x))%R.
Proof.
  intros x (h1,h2).
  exact (Reals.R_sqrt.sqrt_more x h1 h2).
Qed.

(* Why3 goal *)
Lemma sqrt_0 : ((Reals.R_sqrt.sqrt 0%R) = 0%R).
Proof.
  exact Reals.R_sqrt.sqrt_0.
Qed.

(* Why3 goal *)
Lemma sqrt_1 : ((Reals.R_sqrt.sqrt 1%R) = 1%R).
Proof.
  exact Reals.R_sqrt.sqrt_1.
Qed.

