proposition: Lemma derive_Rball_mult: 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 * g x + f 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_mult ; assumption | ring]. Qed.
imports: Rbase Ranalysis Rinterval Rfunctions Rfunction_def Rfunction_facts Ranalysis_def Ranalysis_def_simpl Ranalysis_continuity MyRIneq MyR_dist Lra Tactics