Require Export GeoCoq.Utils.triples.
Section T.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** We need a notion of line. *)
Definition Line := @Couple Tpoint.
Definition Lin := build_couple Tpoint.
Definition IncidentL := fun A l => Col A (P1 l) (P2 l).
(** * Group I Combination *)
(** For every pair of distinct points there is a line containing them. *)

(* Specifications: *)
Lemma axiom_line_existence : forall A B, A<>B -> exists l, IncidentL A l /\ IncidentL B l.
Definition EqL : relation Line := fun l m => forall X, IncidentL X l <-> IncidentL X m.