proposition: Lemma sum_n_m_zero (a : nat -> G) (n m : nat) : (m < n)%nat -> sum_n_m a n m = zero.
proof: Proof. intros Hnm. rewrite /sum_n_m. elim: n m a Hnm => [ | n IH] m a Hnm. by apply Nat.nlt_0_r in Hnm. case: m Hnm => [|m] Hnm //. rewrite -iter_nat_S. apply IH. by apply Nat.succ_lt_mono. Qed.
imports: Coq(Reals Psatz ssreflect) Rcomplements Rbar Markov Iter Lub