Section T18.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.
Variable SS U1 U2 : Tpoint.
Variable orthonormal_grid : Cs O E SS U1 U2.
Definition F : Type := {P : Tpoint | Col O E P}.
Definition EqF (x y : F) := (proj1_sig x) = (proj1_sig y).
Instance eqF_Reflexive : Reflexive EqF.

(* Specifications: *)
Lemma eq_dec_F : forall A B, EqF A B \/ ~ EqF A B.
Lemma neg_and_eqF : forall A B C D,
~ (EqF A B /\ EqF C D) <-> ~ EqF A B \/ ~ EqF C D.