Section Formula_Decideability.
Definition language_decideable :=
((forall x y : Functions L, {x = y} + {x <> y}) *
(forall x y : Relations L, {x = y} + {x <> y}))%type.
Hypothesis language_dec : language_decideable.
Let nilTermsHelp : forall n : nat, n = 0 -> Terms n.
intros.
induction n as [| n Hrecn].
apply Tnil.
discriminate H.
Defined.

Lemma nilTerms : forall x : Terms 0, Tnil = x.