Section EXTRA1.
Definition inconsistent {L : language} (Gamma : ensemble (frm L)) : Prop :=
forall p, Gamma ⊢ p.
Context {L : language}.
Proof with repeat ((now left) || right).
eapply NegationE, ContradictionI.
- eapply DisjunctionI2, NegationI, ContradictionI.
+ eapply DisjunctionI1, ByAssumption...
+ eapply ByAssumption...
- eapply ByAssumption...
Qed.

Lemma Cut_property (Gamma : ensemble (frm L)) A B
(INFERS : Gamma ⊢ A)
(IMPLY : E.insert A Gamma ⊢ B)
: Gamma ⊢ B.