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diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_eval.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_eval.ma
index 1b58977b0..3a8971fd8 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_eval.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_eval.ma
@@ -19,17 +19,17 @@ include "basic_2/dynamic/nta_preserve.ma".
 
 (* Properties with evaluations for rt-transition on terms *******************)
 
-lemma nta_typecheck_dec (a) (h) (G) (L): ac_props a →
-      ∀T,U. Decidable … (⦃G,L⦄ ⊢ T :[a,h] U).
+lemma nta_typecheck_dec (h) (a) (G) (L): ac_props a →
+      ∀T,U. Decidable … (⦃G,L⦄ ⊢ 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): ac_props a →
-      ∨∨ ∃U. ⦃G,L⦄ ⊢ T :[a,h] U
-       | ∀U. (⦃G,L⦄ ⊢ T :[a,h] U → ⊥).
-#a #h #G #L #T #Ha
-elim (cnv_dec … h G L T Ha) -Ha
+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-.