Notation ring_rw_correct :=
 (ring_rw_correct Rsth Reqe ARth CRmorph pow_th cdiv_th get_sign_spec).Notation ring_rw_pow_correct :=
 (ring_rw_pow_correct Rsth Reqe ARth CRmorph pow_th cdiv_th get_sign_spec).Notation ring_correct :=
 (ring_correct Rsth Reqe ARth CRmorph pow_th cdiv_th).(* simplify a field expression into a fraction *)
Definition display_linear l num den :=
  let lnum := NPphi_dev l num in
    match den with
    | Pc c => if ceqb c cI then lnum else lnum / NPphi_dev l den
    | _ => lnum / NPphi_dev l den
    end.Definition display_pow_linear l num den :=
  let lnum := NPphi_pow l num in
    match den with
    | Pc c => if ceqb c cI then lnum else lnum / NPphi_pow l den
    | _ => lnum / NPphi_pow l den
    end.

Theorem Field_simplify_eq_correct : forall n l lpe fe1 fe2, Ninterp_PElist l lpe -> forall lmp, Nmk_monpol_list lpe = lmp -> forall nfe1, Fnorm fe1 = nfe1 -> forall nfe2, Fnorm fe2 = nfe2 -> forall den, split (denum nfe1) (denum nfe2) = den -> NPphi_dev l (Nnorm n lmp (num nfe1 * right den)) == NPphi_dev l (Nnorm n lmp (num nfe2 * left den)) -> PCond l (condition nfe1 ++ condition nfe2) -> FEeval l fe1 == FEeval l fe2.