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_aux_ok l fe1 fe2 den : FEeval l fe1 == FEeval l fe2 -> split (denum (Fnorm fe1)) (denum (Fnorm fe2)) = den -> PCond l (condition (Fnorm fe1) ++ condition (Fnorm fe2)) -> (num (Fnorm fe1) * right den) @ l == (num (Fnorm fe2) * left den) @ l.