(* simplify a field equation : generate the crossproduct and simplify polynomials *)
(** This allows rewriting modulo the simplification of PEeval on PMul *)
Declare Equivalent Keys PEeval rmul.

Theorem Field_simplify_eq_pow_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_pow l (Nnorm n lmp (num nfe1 * right den)) ==
NPphi_pow l (Nnorm n lmp (num nfe2 * left den)) ->
PCond l (condition nfe1 ++ condition nfe2) ->
FEeval l fe1 == FEeval l fe2.