(*To prove the strong contructive result we need the decidability of T*)

(* Specifications: *)
Theorem Rosser'sIncompleteness :
(forall x : Formula, mem _ T x \/ ~ mem _ T x) ->
exists f : Formula,
(forall v : nat, ~ In v (freeVarFormula LNN f)) /\
(SysPrf T f \/ SysPrf T (notH f) -> Inconsistent LNN T).
Theorem Rosser'sIncompleteness :
(forall x : Formula, mem _ T x \/ ~ mem _ T x) ->
exists f : Formula,
(forall v : nat, ~ In v (freeVarFormula LNT f)) /\
(SysPrf T f \/ SysPrf T (notH f) -> Inconsistent LNT T).