proposition: Lemma gt_pred_ceil x : x \is Rreal -> (ceil x - 1)%:~R < x.
proof: Proof. by move=> /ceil_itv /andP[]. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order ssralg poly ssrnum ssrint)