proposition: Lemma derivable_pt_scal : forall f (a x:R), derivable_pt f x -> derivable_pt (mult_real_fct a f) x.
proof: Proof. unfold derivable_pt; intros f1 a x X. elim X; intros. exists (a * x0). apply derivable_pt_lim_scal; assumption. Qed.
imports: Rbase Rfunctions Rlimit Rderiv