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

Lemma EquationE (Gamma : ensemble (frm L)) x t1 t2 A
(INFERS1 : Gamma ⊢ Eqn_frm t1 t2)
(INFERS2 : Gamma ⊢ subst_frm (one_subst x t1) A)
: Gamma ⊢ subst_frm (one_subst x t2) A.