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

Lemma extend_infers (Gamma : ensemble (frm L)) (Gamma' : ensemble (frm L)) (C : frm L)
(INFERS : Gamma ⊢ C)
(SUBSET : Gamma \subseteq Gamma')
: Gamma' ⊢ C.