Definition Qeval_formula (e:PolEnv Q) (k: Tauto.kind) (ff : Formula Q) :=
let (lhs,o,rhs) := ff in Qeval_op2 k o (Qeval_expr e lhs) (Qeval_expr e rhs).
Definition Qeval_formula' :=
eval_formula  Qplus Qmult Qminus Qopp Qeq Qle Qlt (fun x => x) (fun x => x) (pow_N 1 Qmult).

(* Specifications: *)
Lemma Qeval_formula_compat : forall env b f, Tauto.hold b (Qeval_formula env b f) <-> Qeval_formula' env f.
Definition Qeval_nformula :=
eval_nformula 0 Qplus Qmult  Qeq Qle Qlt (fun x => x) .