unfold Cong in *.
induction H.
left; intuition.
apply congH_sym.
assumption.
assumption.
right.
tauto.
Qed.

(* Specifications: *)
Lemma cong_trans : forall A B C D E F, Cong A B C D -> Cong C D E F -> Cong A B E F.
Lemma betH_not_congH : forall A B C, BetH A B C ->  ~ CongH A B A C.
Lemma congH_permlr : forall A B C D, A<>B -> C<>D -> CongH A B C D -> CongH B A D C.
Lemma congH_perms : forall A B C D,
A<>B -> C<>D ->
CongH A B C D ->
(CongH B A C D /\ CongH A B D C /\ CongH C D A B /\
CongH D C A B /\ CongH C D B A /\ CongH D C B A /\ CongH B A D C).
Lemma congH_perml : forall A B C D,
A <> B -> C <> D -> CongH A B C D ->
CongH B A C D.
Lemma betH_congH3_outH_betH : forall A B C A' B' C',
BetH A B C -> outH A' B' C' -> CongH A C A' C' -> CongH A B A' B' -> BetH A' B' C'.
Lemma outH_sym : forall A B C,
A <> C -> outH A B C -> outH A C B.
Lemma soustraction_betH :
forall A B C A' B' C' : Point,
BetH A B C ->
BetH A' B' C' ->
CongH A B A' B' -> CongH A C A' C' -> CongH B C B' C'.
Lemma ncolH_expand : forall A B C, ~ ColH A B C -> ~ ColH A B C /\ A <> B /\ B <> C /\ A <> C.
Lemma betH_outH__outH : forall A B C D,
BetH A B C -> outH B C D -> outH A C D.