Definition LeF (x y : F) := LeP O E E' (proj1_sig x) (proj1_sig y).Instance leF_Antisymmetric : Antisymmetric F EqF LeF.Instance leF_Transitive : Transitive LeF.

(* Specifications: *)
Lemma coordinates_of_point_f : forall P, {C | Cd O E SS U1 U2 P (fst C) (snd C)}.
Lemma coordinates_of_point_F : forall P, {C: F*F | Cd O E SS U1 U2 P (proj1_sig (fst C)) (proj1_sig (snd C))}.