proposition: Lemma continuity_implies_RiemannInt : forall (f:R -> R) (a b:R), a <= b -> (forall x:R, a <= x <= b -> continuity_pt f x) -> Riemann_integrable f a b.
proof: Proof. intros; destruct (total_order_T a b) as [[Hlt| -> ]|Hgt]; [ apply RiemannInt_P6; assumption | apply RiemannInt_P7 | elim (Rlt_irrefl _ (Rle_lt_trans _ _ _ H Hgt)) ]. Qed.
imports: Rfunctions SeqSeries Ranalysis_reg Rbase RiemannInt_SF RList Lra