Section between_identity_independent.
Inductive Point :=
P0 | P1 | P2 | P3.
Definition Bet (A B C : Point) :=
A = B \/ B = C \/ A = C.
Definition Cong (A B C D : Point) :=
(A = B /\ C = D) \/ (A <> B /\ C <> D).

Lemma not_between_identity : ~ (forall A B, Bet A B A -> A=B).