-lemma nta_inference_dec (a) (h) (G) (L) (T):
- ∨∨ ∃U. ⦃G,L⦄ ⊢ T :[a,h] U
- | ∀U. (⦃G,L⦄ ⊢ T :[a,h] U → ⊥).
-#a #h #G #L #T
-elim (cnv_dec a h G L T)
+lemma nta_inference_dec (h) (a) (G) (L) (T): ac_props a →
+ Decidable (∃U. ❪G,L❫ ⊢ T :[h,a] U).
+#h #a #G #L #T #Ha
+elim (cnv_dec h … G L T Ha) -Ha #HT