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 midpoint_preserves_image : forall A B P P' Q Q' M, A <> B -> Col A B M -> Reflect P P' A B -> Midpoint M P Q -> Midpoint M P' Q' -> Reflect Q Q' A B.