unfold Same_dir in H.
induction H.
tauto.
ex_and H D.
apply null_vector in H0.
subst D.
unfold Out in H.
tauto.
Qed.

Lemma plgf_out_plgf :
forall A B C D B' C',
Parallelogram_flat A B C D ->
Out A B B' ->
Out D C C' ->
Cong A B' D C' ->
Parallelogram_flat A B' C' D.