Definition ty_ex (F:pred world -> pred world) : pred world :=
EX tau:pred world, !!(boxy extendM tau) && F tau.

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).