proposition: Lemma RiemannInt_P29 : forall (f:R -> R) a b (h:a <= b) (C0:forall x:R, a <= x <= b -> continuity_pt f x), antiderivative f (primitive h (FTC_P1 h C0)) a b.
proof: Proof. intro f; intros; unfold antiderivative; split; try assumption; intros; assert (H0 := RiemannInt_P28 h C0 H); assert (H1 : derivable_pt (primitive h (FTC_P1 h C0)) x); [ unfold derivable_pt; split with (f x); apply H0 | split with H1; symmetry ; apply derive_pt_eq_0; apply H0 ]. Qed.
imports: Rfunctions SeqSeries Ranalysis_reg Rbase RiemannInt_SF RList Lra