(** 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.