Ltac CopR :=
 let tpoint := constr:(Tpoint) in
 let col := constr:(Col) in
 let cop := constr:(Coplanar) in
   assert_ncols; Cop_refl tpoint col cop.

Lemma ex_per_cong : forall A B C D X Y, A <> B -> X <> Y -> Col A B C -> ~Col A B D -> exists P, Per P C A /\ Cong P C X Y /\ OS A B P D.