Ltac Col := auto 3 with col.Ltac line A B l Hdiff := let H:=fresh in (assert(H:= line_existence A B Hdiff); destruct H as [l]; spliter).Ltac ColHR :=
 let tpoint := constr:(Point) in
 let col := constr:(ColH) in
   Col_refl tpoint col.Ltac two_points l X Y := assert(_H := two_points_on_line l); destruct _H as [X _H]; destruct _H as [Y _H]; spliter.

Lemma inter_incid_uniquenessH : forall P X Y l m, ~IncidL P l -> IncidL P m -> IncidL X l -> IncidL Y l -> IncidL X m -> IncidL Y m -> X = Y.