proposition: Lemma sum_INR : forall n, sum_f_R0 INR n = INR n * (INR n + 1) / 2.
proof: Proof. elim => [ | n IH] ; rewrite /sum_f_R0 -/sum_f_R0 ?S_INR /=. rewrite /Rdiv ; ring. rewrite IH ; field. Qed.
imports: Coq(Reals Psatz ssreflect) Coq(ssrbool) mathcomp(seq)