Definition wring (sz : nat) : ring_theory (wzero sz) (wone sz) (@wplus sz) (@wmult sz) (@wminus sz) (@wneg sz) (@eq _) :=
  mk_rt _ _ _ _ _ _ _
  (@wplus_unit _) (@wplus_comm _) (@wplus_assoc _)
  (@wmult_unit _) (@wmult_comm _) (@wmult_assoc _)
  (@wmult_plus_distr _) (@wminus_def _) (@wminus_inv _).

Lemma weqb_false: forall sz (a b: word sz), weqb a b = false -> a <> b.