Section HilbertContext_2.
Context `{Hi:Hilbert_neutral_dimensionless}.
Definition Cong A B C D := (CongH A B C D /\ A <> B /\ C <> D) \/ (A = B /\ C = D).
(****************** between_identity ************************)
(************************************************************)
(***************************** cong_identity ***********************)
(************************ cong_inner_transitivity ****************************)
intros.
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 out_construction : forall A B X Y, X <> Y -> A <> B -> exists C, CongH A C X Y /\ (outH A B C).