proposition: Lemma inject_Q_AR_wd : forall q r : Q, q == r -> inject_Q_AR q = inject_Q_AR r.
proof: Proof. intros q r qreq e1 e2. simpl. destruct aq_dense_embedding. unfold cast. rewrite Qplus_0_r. apply ball_triangle with (b:=q). apply dense_inverse. simpl. rewrite qreq. change (Qball (` e2) r (AQtoQ (app_inverse AQtoQ r e2))). apply ball_sym. apply dense_inverse. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity Coq.Program.Program Coq.setoid_ring.Ring Coq.QArith.Qabs CoRN.stdlib_omissions.Q MathClasses.misc.workaround_tactics CoRN.model.totalorder.QMinMax CoRN.model.totalorder.QposMinMax CoRN.util.Qdlog CoRN.metric2.Complete CoRN.metric2.Prelength CoRN.model.metric2.Qmetric CoRN.metric2.MetricMorphisms CoRN.reals.fast.CRArith CoRN.reals.fast.CRpower MathClasses.implementations.stdlib_binary_naturals MathClasses.orders.minmax MathClasses.implementations.positive_semiring_elements CoRN.reals.faster.ApproximateRationals CoRN.reals.faster.AQmetric