proposition: Lemma ltB_incR n q (p:BITS n) : ltB p q -> ltB p (p +# 1).
proof: Proof. move => H. have LTB := ltB_bound H. rewrite ltB_nat addB1 toNat_incB. case E: (p == ones _). + rewrite (eqP E) in LTB. by rewrite toNat_ones ltnn in LTB. + apply ltnSn. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq fintype tuple zmodp div) ssrextra.tuple ssrextra.nat spec spec.properties operations mathcomp(ssralg)