Definition prim (f:nat -> value) : expr -> expr :=
  Prim (val_to_exp oo f).

Lemma T_ExtI : forall G e (X:pred world -> pred world) tau (Hext : forall tau, boxy extendM tau -> boxy extendM (X tau)), boxy extendM tau -> Typ G e (X tau) -> Typ G e (ty_ex X).