(* Correctness lemmas of reflexive tactics *)
Notation Ninterp_PElist :=
(interp_PElist rO rI radd rmul rsub ropp req phi Cp_phi rpow).
Notation Nmk_monpol_list :=
(mk_monpol_list cO cI cadd cmul csub copp ceqb cdiv).

(* Specifications: *)
Theorem Fnorm_ok:
forall n l lpe fe,
Ninterp_PElist l lpe ->
Peq ceqb (Nnorm n (Nmk_monpol_list lpe) (num (Fnorm fe))) (Pc cO) = true ->
PCond l (condition (Fnorm fe)) ->  FEeval l fe == 0.