unfold Same_dir.
right.
assert(HH:=vector_construction A B B).
ex_and HH C'.
exists C'.
split.
2: auto.
unfold EqV in H2.
induction H2.
2:tauto.
induction H2.
apply plgs_par_strict in H2.
spliter.
apply False_ind.
apply H3.
exists B.
split; Col.
assert(HH:= H2).
unfold Parallelogram_flat in HH.
apply plgf_bet in H2.
spliter.
unfold Out.
repeat split.
auto.
intro.
subst C'.
apply cong_identity in H5.
contradiction.
induction H2.
assert(Bet B A B).
spliter.
apply (outer_transitivity_between2 _ C').
Between.
auto.
induction H7.
auto.
tauto.
apply between_identity in H8.
subst B.
tauto.
induction H2.
assert(Bet B A B).
spliter.
apply (outer_transitivity_between _ _ C').
apply H2.
auto.
induction H7.
auto.
tauto.
apply between_identity in H8.
subst B.
tauto.
induction H2.
assert( A = C' \/ Midpoint B A C').
apply l7_20.
Col.
Cong.
induction H8.
induction H7.
tauto.
tauto.
unfold Midpoint in H8.
spliter.
apply (l5_2 A); auto.
assert( A = C' \/ Midpoint B A C').
apply l7_20.
Col.
Cong.
induction H8.
induction H7.
tauto.
tauto.
unfold Midpoint in H8.
spliter.
apply (l5_2 A); auto.
Qed.

Lemma plg_opp_dir : forall A B C D, Parallelogram A B C D -> Same_dir A B D C.
intros.