proposition: Lemma ltz_divLR m n d : d > 0 -> ((m %/ d)%Z < n) = (m < n * d).
proof: Proof. move=> d_gt0; apply/idP/idP. by rewrite -[_ < n]lezD1 -(ler_pM2r d_gt0); exact/lt_le_trans/ltz_ceil. by rewrite -(ltr_pM2r d_gt0 _ n); apply/le_lt_trans/lez_floor; rewrite gt_eqF. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly ssrnum ssrint archimedean rat matrix) mathcomp(polydiv perm zmodp mxalgebra vector)