Ltac Bet := auto 3 with bet.

(* Specifications: *)
Lemma betH_distincts : forall A B C, BetH A B C -> A <> B /\ B <> C /\ A <> C.
Lemma congH_perm : forall A B, A<>B -> CongH A B B A.
Lemma congH_refl : forall A B, A<>B -> CongH A B A B.
Lemma congH_sym : forall A B C D, A<>B -> CongH A B C D -> CongH C D A B.