Add Field GeometricField : fieldF.
Global Instance Fops: (@Ring_ops F OF OneF AddF MulF SubF OppF EqF) := {}.
Global Instance FRing : (Ring (Ro:=Fops)).
Global Instance Fintegral : (Integral_domain (Rcr:=Fcri)).

Lemma neqO_mul_neqO : forall x y:F,  ~ x =F= 0 -> ~ y =F= 0 -> ~ x * y =F= 0.