Section CPS.
Hypothesis Σ:Set.
Hypothesis T:Type.
Hypothesis InT:(ExecState Σ)->T->Prop.
Definition isClosed(tm:TM Σ)(S:T):Prop :=
forall st0,
InT st0 S ->
exists n,
exists st1,
Steps Σ tm (1+n) st0 st1 /\
InT st1 S.

Lemma Closed_NonHalt tm S st:
InT st S ->
isClosed tm S ->
forall n:nat,
exists m:nat,
n<=m /\
exists st0,
Steps Σ tm m st st0 /\
InT st0 S.