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_sym : forall A B X, exists Y, (Perp A B X Y \/ X = Y) /\ (exists M, Col A B M /\ Midpoint M X Y).