simple induction 1.
tauto.
intro.
case vs.
inversion 1.
intros.
case a.
apply (T0 A B w nil); auto.
apply (T0 B A w nil); auto.
auto.
Defined.
Hint Resolve lemma4.

Theorem letter_neq : forall a b c : letter, a <> b -> c <> a -> c = b.
intros a b c; case a; case b; case c; tauto.