Hint Resolve type_def_incr: ty.

(* Specifications: *)
Lemma type_def_sound:
forall te x ty e e', type_def e x ty = OK e' -> satisf te e' -> T.sub ty (te x).
Lemma type_defs_incr:
forall te xl tyl e e', type_defs e xl tyl = OK e' -> satisf te e' -> satisf te e.