Remark type_expect_incr:
forall e ty1 ty2 e' te, type_expect e ty1 ty2 = OK e' -> S.satisf te e' -> S.satisf te e.
Hint Resolve type_expect_incr: ty.

Lemma type_expect_sound:
forall e ty1 ty2 e', type_expect e ty1 ty2 = OK e' -> ty1 = ty2.