Section Translate_Proof.
Variable U : fol.System LNN.
Variable V : System.
Hypothesis
AxiomsOK :
forall f : fol.Formula LNN,
mem _ U f ->
exists Axm : Formulas,
(exists prf : Prf LNT Axm (LNN2LNT_formula f),
(forall g : Formula, In g Axm -> mem _ V g)) /\
forall v, In v (freeVarListFormula LNT Axm) -> (In v (freeVarFormula LNN f)).
End Translate_Proof.

Lemma translateProof
: forall (U : fol.System LNN) (V : System),
ClosedSystem LNT V ->
(forall f : fol.Formula LNN,
mem (fol.Formula LNN) U f -> SysPrf V (LNN2LNT_formula f)) ->
forall f : fol.Formula LNN,
folProof.SysPrf LNN U f -> SysPrf V (LNN2LNT_formula f).