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)).

(* Specifications: *)
Lemma subF__eq0 : forall x y:F, x - y =F= 0 <-> x =F= y.
Lemma neqO_mul_neqO : forall x y:F,  ~ x =F= 0 -> ~ y =F= 0 -> ~ x * y =F= 0.
Lemma Cd_Cd_EqF : forall P Px1 Py1 Px2 Py2,
Cd O E SS U1 U2 P (proj1_sig Px1) (proj1_sig Py1) ->
Cd O E SS U1 U2 P (proj1_sig Px2) (proj1_sig Py2) ->
Px1 =F= Px2 /\ Py1 =F= Py2.