proposition: Lemma ceil_itv x : x \is Rreal -> (ceil x - 1)%:~R < x <= (ceil x)%:~R.
proof: Proof. by move=> Rx; rewrite -opprD !mulrNz ltrNl lerNr andbC floor_itv ?realN. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order ssralg poly ssrnum ssrint)