(** 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.

(* Specifications: *)
Lemma incident_eq : forall A B l, forall H : A<>B, IncidentL A l -> IncidentL B l -> (Lin A B H) =l= l.
Lemma eq_transitivity : forall l m n, l =l= m -> m =l= n -> l =l= n.
Lemma eq_reflexivity : forall l, l =l= l.
Lemma eq_symmetry : forall l m, l =l= m -> m =l= l.