proposition: Lemma limit_def `{CompleteMetricSpaceClass} (f : RegularFunction) : forall e : Q, 0 < e -> ball e (f e) (lim f).
proof: Proof. intros e2 A2. apply mspc_symm; apply mspc_closed. intros e1 A1. change (lim f) with (reg_unit (lim f) e1). rewrite plus_comm. rapply (surjective reg_unit (inv := lim)); trivial; reflexivity. 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