Lemma image_gen_preserves_inter : forall A B C D I A' B' C' D' I' X Y, Reflect A A' X Y -> Reflect B B' X Y -> Reflect C C' X Y -> Reflect D D' X Y -> ~ Col A B C -> C <> D -> Col A B I -> Col C D I -> Col A' B' I' -> Col C' D' I' -> Reflect I I' X Y.