(*Trace has form ((v,s, formula_input), formula_output, [subTrace1], [subTrace2])*)
Definition codeNewVar (l : nat) : nat :=
evalStrongRec 0
(fun n Hrecs : nat =>
switchPR n
(max (S (cPairPi1 (pred n)))
(codeNth (n - S (cPairPi2 (pred n))) Hrecs)) 0) l.

Lemma codeNewVarCorrect :
forall l : list nat, codeNewVar (codeList l) = newVar l.