(* Julien Narboux *)
(* Formalization of *)
(* Tarski's axiomatic *)
Require Export  Ch03_between_properties.
Proof with Tarski.
intros.
unfold IFSC in H.
intuition.
cases_equality A C.
treat_equalities...
assert (exists E, Bet A C E /\ C <> E)...
DecompExAnd H6 E.
assert (exists E', Bet A' C' E' /\ Cong C' E' C E)...
DecompExAnd H6 E'.
assert (Cong E D E' D').
eapply five_segments_with_def.
assert (OFSC A C E D A' C' E' D').
unfold OFSC.
intuition.
apply H6.
assumption.
assert (OFSC E C B D E' C' B' D').
unfold OFSC.
intuition;esTarski.
esTarski.
Qed.

Lemma l4_3 :  forall A B C A' B' C',
Bet A B C -> Bet A' B' C' ->
Cong A C A' C' -> Cong B C B' C' -> Cong A B A' B'.