Section Rosser's_Incompleteness.
Definition codeFormula := codeFormula LNT codeLNTFunction codeLNTRelation.
Variable T : System.
Definition T' : fol.System LNN :=
Union _ NN
(fun x : fol.Formula LNN => mem _ T (LNN2LNT_formula x)).
Hypothesis extendsPA : Included _ PA T.
Variable repT : Formula.
Variable v0 : nat.
Hypothesis
freeVarRepT : forall v : nat, In v (freeVarFormula LNT repT) -> v = v0.
Hypothesis
expressT1 :
forall f : Formula,
mem _ T f ->
SysPrf T (substituteFormula LNT repT v0 (natToTerm (codeFormula f))).
Hypothesis
expressT2 :
forall f : Formula,
~ mem _ T f ->
SysPrf T
(notH (substituteFormula LNT repT v0 (natToTerm (codeFormula f)))).

Lemma freeVarRepT' :
forall v : nat, In v (freeVarFormula LNN (LNT2LNN_formula repT)) -> v = v0.