proposition: Lemma AQsqrt_correct (a : AQ) : 'AQsqrt a = rational_sqrt ('a).
proof: Proof. unfold AQsqrt. case (decide_rel _); intros E. rewrite rational_sqrt_nonpos. now apply rings.preserves_0. now apply semirings.preserves_nonpos. now apply AQsqrt_pos_correct. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity Coq.setoid_ring.Ring CoRN.stdlib_omissions.Z CoRN.model.totalorder.QposMinMax CoRN.metric2.Complete CoRN.model.metric2.Qmetric Coq.ZArith.ZArith CoRN.util.Qdlog CoRN.reals.fast.CRroot CoRN.reals.faster.ARabs MathClasses.interfaces.abstract_algebra MathClasses.theory.shiftl MathClasses.theory.nat_pow MathClasses.theory.int_pow CoRN.reals.faster.ARArith