Definition Qeval_expr' := eval_pexpr  Qplus Qmult Qminus Qopp (fun x => x) (fun x => x) (pow_N 1 Qmult).

(* Specifications: *)
Lemma QNpower : forall r n, r ^ Z.of_N n = pow_N 1 Qmult r n.
Lemma Qeval_expr_compat : forall env e, Qeval_expr env e = Qeval_expr' env e.
Definition Qeval_pop2 (o : Op2) : Q -> Q -> Prop :=
match o with
| OpEq =>  Qeq
| OpNEq => fun x y  => ~ x == y
| OpLe => Qle
| OpGe => fun x y => Qle y x
| OpLt => Qlt
| OpGt => fun x y => Qlt y x
end.