(* 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_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.