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 CPS_correct tm S st:
InT st S ->
isClosed tm S ->
~Halts _ tm st.