proposition: Lemma derivable_pt_plus : forall f1 f2 (x:R), derivable_pt f1 x -> derivable_pt f2 x -> derivable_pt (f1 + f2) x.
proof: Proof. unfold derivable_pt; intros f1 f2 x X X0. elim X; intros. elim X0; intros. exists (x0 + x1). apply derivable_pt_lim_plus; assumption. Qed.
imports: Rbase Rfunctions Rlimit Rderiv