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)))).

(* Specifications: *)
Lemma freeVarRepT' :
forall v : nat, In v (freeVarFormula LNN (LNT2LNN_formula repT)) -> v = v0.
Lemma Tprf2T'prf :
forall f : Formula, SysPrf T f -> folProof.SysPrf LNN T' (LNT2LNN_formula f).
Lemma expressT'1 :
forall f : Formula,
mem _ T f ->
folProof.SysPrf LNN T'
(substituteFormula LNN (LNT2LNN_formula repT) v0
(natToTermLNN (codeFormula f))).
Lemma expressT'2 :
forall f : Formula,
~ mem _ T f ->
folProof.SysPrf LNN T'
(fol.notH LNN
(substituteFormula LNN (LNT2LNN_formula repT) v0
(natToTermLNN (codeFormula f)))).