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_plgf_bet :
forall A B C D B' C',
Parallelogram_flat A B C D ->
Bet A B B' ->
Parallelogram_flat A B' C' D ->
Bet D C C'.