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

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).