Require Export PA.
Unset Standard Proposition Elimination Names.

Lemma paZeroOrSucc :
forall t : Term,
SysPrf PA
(orH (equal t Zero)
(existH (newVar (0 :: freeVarTerm LNT t))
(equal t (Succ (var (newVar (0 :: freeVarTerm LNT t))))))).