proposition: Lemma AQsqrt_mid_bounded_raw_square_upper_bound (n : N) : AQsqrt_mid_bounded_raw n ^ (2:N) ≤ a.
proof: Proof. rewrite AQsqrt_mid_bounded_spec. apply rings.nonneg_minus_compat; [| reflexivity]. now apply shiftl_nonneg, AQsqrt_loop_fst_nonneg. 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