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 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.