Add Zify BinOp Op_nat_eqb.
#[global]
Instance Op_nat_leb : BinOp Nat.leb :=
{ TBOp := Z.leb; TBOpInj := Z_of_nat_leb_iff }.
Add Zify BinOp Op_nat_leb.
#[global]
Instance Op_nat_ltb : BinOp Nat.ltb :=
{ TBOp := Z.ltb; TBOpInj := Z_of_nat_ltb_iff }.
Add Zify BinOp Op_nat_ltb.

Lemma b2n_b2z x : Z.of_nat (Nat.b2n x) = Z.b2z x.
#[global]
Instance Op_b2n : UnOp Nat.b2n :=
{ TUOp := Z.b2z; TUOpInj := b2n_b2z }.