Section EXTRA1.
Definition inconsistent {L : language} (Gamma : ensemble (frm L)) : Prop :=
forall p, Gamma ⊢ p.
Context {L : language}.

Lemma UniversalI (Gamma : ensemble (frm L)) x y A
(FRESH1 : forall p, p \in Gamma -> is_free_in_frm y p = false)
(FRESH2 : is_free_in_frm y (All_frm x A) = false)
(INFERS1 : Gamma ⊢ subst_frm (one_subst x (Var_trm y)) A)
: Gamma ⊢ All_frm x A.