proposition: Lemma CRsqrt_pos : forall x : CR, (0 <= x -> 0 <= CRsqrt x)%CR.
proof: Proof. intros x H e1. simpl. unfold Cap_raw; simpl. unfold Cjoin_raw; simpl. rewrite Qplus_0_r. apply (Qle_trans _ 0). apply (Qopp_le_compat 0 (`e1)). apply Qpos_nonneg. apply rational_sqrt_nonneg. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.reals.Q_in_CReals CoRN.reals.fast.CRpower CoRN.reals.fast.CRArith CoRN.reals.fast.CRIR CoRN.reals.NRootIR CoRN.model.totalorder.QMinMax CoRN.model.totalorder.QposMinMax CoRN.model.metric2.Qmetric Coq.QArith.Qpower CoRN.model.ordfields.Qordfield CoRN.reals.fast.Compress Coq.NArith.Ndigits CoRN.reals.fast.PowerBound CoRN.transc.RealPowers CoRN.reals.fast.ContinuousCorrect CoRN.tactics.Qauto CoRN.tactics.CornTac MathClasses.interfaces.abstract_algebra