(* Properties with evaluations for rt-transition on terms *******************)
-lemma nta_typecheck_dec (a) (h) (G) (L):
+lemma nta_typecheck_dec (a) (h) (G) (L): ac_props a →
∀T,U. Decidable … (⦃G,L⦄ ⊢ T :[a,h] U).
/2 width=1 by cnv_dec/ qed-.
(* Basic_1: uses: ty3_inference *)
-lemma nta_inference_dec (a) (h) (G) (L) (T):
+lemma nta_inference_dec (a) (h) (G) (L) (T): ac_props a →
∨∨ ∃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)
+#a #h #G #L #T #Ha
+elim (cnv_dec … h G L T Ha) -Ha
[ /3 width=1 by cnv_nta_sn, or_introl/
| /4 width=2 by nta_fwd_cnv_sn, or_intror/
]