proposition: Lemma ceil_def x m : (m - 1)%:~R < x <= m%:~R -> ceil x = m.
proof: Proof. move=> Hx; apply/eqP; rewrite eqr_oppLR; apply/eqP/floor_def. by rewrite lerNr ltrNl andbC -!mulrNz opprD opprK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order ssralg poly ssrnum ssrint)