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

Lemma b2n_b2z x : Z.of_nat (Nat.b2n x) = Z.b2z x.