proposition: Lemma FTC_Riemann : forall (f:C1_fun) (a b:R) (pr:Riemann_integrable (derive f (diff0 f)) a b), RiemannInt pr = f b - f a.
proof: Proof. intro f; intros; destruct (Rle_dec a b) as [Hle|Hnle]; [ apply RiemannInt_P33; assumption | assert (H : b <= a); [ auto with real | assert (H0 := RiemannInt_P1 pr); rewrite (RiemannInt_P8 pr H0); rewrite (RiemannInt_P33 _ H0 H); ring ] ]. Qed.
imports: Rfunctions SeqSeries Ranalysis_reg Rbase RiemannInt_SF RList Lra