proposition: Lemma radius_nonneg (x y : X) (e : Q) : ball e x y -> 0 ≤ e.
proof: Proof. intro A. destruct (le_or_lt 0 e) as [A1 | A1]; [trivial |]. contradict A; now apply mspc_negative. 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