proposition: Lemma func_ball_proper : Proper ((=) ==> (≡) ==> (≡) ==> iff) (ball (X := T)).
proof: Proof. intros q1 q2 A1 f1 f2 A2 g1 g2 A3; rewrite A2, A3. split; intros A4 x; [rewrite <- A1 | rewrite A1]; apply A4. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity Coq.QArith.QArith MathClasses.theory.setoids MathClasses.theory.products MathClasses.implementations.stdlib_rationals MathClasses.interfaces.abstract_algebra MathClasses.implementations.QType_rationals MathClasses.interfaces.additional_operations CoRN.tactics.Qauto Coq.QArith.QOrderedType MathClasses.theory.rings MathClasses.theory.dec_fields MathClasses.orders.rings MathClasses.orders.dec_fields MathClasses.theory.nat_pow MathClasses.interfaces.naturals MathClasses.interfaces.orders CoRN.reals.fast.CRGeometricSum