(* Properties with evaluations for rt-transition on terms *******************)
-lemma nta_typecheck_dec (a) (h) (G) (L):
- â\88\80T,U. Decidable â\80¦ (â¦\83G,Lâ¦\84 â\8a¢ T :[a,h] U).
+lemma nta_typecheck_dec (h) (a) (G) (L): ac_props a →
+ â\88\80T,U. Decidable â\80¦ (â\9dªG,Lâ\9d« â\8a¢ T :[h,a] U).
/2 width=1 by cnv_dec/ qed-.
(* Basic_1: uses: ty3_inference *)
-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
[ /3 width=1 by cnv_nta_sn, or_introl/
-| /4 width=2 by nta_fwd_cnv_sn, or_intror/
+| @or_intror * #U #HTU
+ /3 width=2 by nta_fwd_cnv_sn/
]
qed-.