unfold disjoint.
intro.
destruct H0 as [P []].
assert(HP:= betH_trans0 A P B C H0 H).
spliter.
apply between_only_one' in H1.
spliter.
contradiction.
Qed.

Lemma construction_uniqueness : forall A B D E,
BetH A B D -> BetH A B E -> CongH B D B E -> D = E.