unfold outH in H.
induction H.
apply between_col in H.
auto.
induction H.
apply between_col in H.
Col.
spliter.
subst C.
Col.
Qed.

Lemma same_side_prime__plane : forall A B C D, same_side' A B C D ->
exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.