Definition Mixin :=
   NumMixin lez_norm_add ltz_add eq0_normz (in2W lez_total) normzM
            lez_def ltz_def.Canonical int_numDomainType := NumDomainType int intOrdered.Mixin.Canonical int_realDomainType := RealDomainType int (intOrdered.lez_total 0).Implicit Types x y z : R.

(* Specifications: *)
Lemma lez_nat m n : (m <= n :> int) = (m <= n)%N.
Lemma ltz_nat m n : (m < n :> int) = (m < n)%N.