proposition: Lemma derive_Rball_plus: forall f g c r x prf prg prfg, derive_Rball c r (f + g)%F prfg x = derive_Rball c r f prf x + derive_Rball c r g prg x.
proof: Proof. intros ; unfold derive_Rball ; destruct (in_Rball_dec c r x) as [x_in | x_nin] ; [apply derive_pt_Rball_plus ; assumption | rewrite Rplus_0_r ; reflexivity]. Qed.
imports: Rbase Ranalysis Rinterval Rfunctions Rfunction_def Rfunction_facts Ranalysis_def Ranalysis_def_simpl Ranalysis_continuity MyRIneq MyR_dist Lra Tactics