proposition: Lemma mspc_triangle' : ∀ (q1 q2 : Q) (x2 x1 x3 : X) (q : Q), q1 + q2 = q → ball q1 x1 x2 → ball q2 x2 x3 → ball q x1 x3.
proof: Proof. intros q1 q2 x2 x1 x3 q A1 A2 A3. rewrite <- A1. eapply mspc_triangle; eauto. 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