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 Incidence *)
(** For every pair of distinct points there is a line containing them. *)
(** We need a notion of equality over lines. *)
Definition EqL : relation Line := fun l m => forall X, IncidentL X l <-> IncidentL X m.
Infix "=l=" := EqL (at level 70):type_scope.

Lemma incident_eq : forall A B l, forall H : A<>B,
IncidentL A l -> IncidentL B l ->
(Lin A B H) =l= l.