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 five_segment : forall A A' B B' C C' D D',
Cong A B A' B' ->
Cong B C B' C' ->
Cong A D A' D' ->
Cong B D B' D' ->
Bet A B C -> Bet A' B' C' -> A <> B -> Cong C D C' D'.