proposition: Lemma ltz_ceil m d : d > 0 -> m < ((m %/ d)%Z + 1) * d.
proof: Proof. by case: d => // d d_gt0; rewrite mulrDl mul1r -ltrBlDl ltz_mod ?Order.POrderTheory.gt_eqF. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq choice fintype order bigop ssralg) mathcomp(div ssrnum ssrint rat prime path binomial) mathcomp(tuple finset) gaia(fibm)