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diff --git a/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma b/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
index 46ba2cef2..d66a9c520 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
@@ -22,14 +22,65 @@ inductive term: Type[0] ≝
   | TPair: item2 → term → term → term (* binary item construction *)
 .
 
-interpretation "sort (term)" 'Star k = (TAtom (Sort k)).
+interpretation "term construction (atomic)"
+   'Item0 I = (TAtom I).
 
-interpretation "local reference (term)" 'LRef i = (TAtom (LRef i)).
+interpretation "term construction (binary)"
+   'SnItem2 I T1 T2 = (TPair I T1 T2).
 
-interpretation "term construction (atomic)" 'SItem I = (TAtom I).
+interpretation "term binding construction (binary)"
+   'SnBind2 I T1 T2 = (TPair (Bind2 I) T1 T2).
 
-interpretation "term construction (binary)" 'SItem I T1 T2 = (TPair I T1 T2).
+interpretation "term flat construction (binary)"
+   'SnFlat2 I T1 T2 = (TPair (Flat2 I) T1 T2).
 
-interpretation "term binding construction (binary)" 'SBind I T1 T2 = (TPair (Bind I) T1 T2).
+interpretation "sort (term)"
+   'Star k = (TAtom (Sort k)).
 
-interpretation "term flat construction (binary)" 'SFlat I T1 T2 = (TPair (Flat I) T1 T2).
+interpretation "local reference (term)"
+   'LRef i = (TAtom (LRef i)).
+
+interpretation "global reference (term)"
+   'GRef p = (TAtom (GRef p)).
+
+interpretation "abbreviation (term)"
+   'SnAbbr T1 T2 = (TPair (Bind2 Abbr) T1 T2).
+
+interpretation "abstraction (term)"
+   'SnAbst T1 T2 = (TPair (Bind2 Abst) T1 T2).
+
+interpretation "application (term)"
+   'SnAppl T1 T2 = (TPair (Flat2 Appl) T1 T2).
+
+interpretation "native type annotation (term)"
+   'SnCast T1 T2 = (TPair (Flat2 Cast) T1 T2).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma discr_tpair_xy_x: ∀I,T,V. ②{I} V. T = V → False.
+#I #T #V elim V -V
+[ #J #H destruct
+| #J #W #U #IHW #_ #H destruct
+  -H >e0 in e1; normalize (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
+  /2 width=1/
+]
+qed-.
+
+(* Basic_1: was: thead_x_y_y *)
+lemma discr_tpair_xy_y: ∀I,V,T. ②{I} V. T = T → False.
+#I #V #T elim T -T
+[ #J #H destruct
+| #J #W #U #_ #IHU #H destruct
+  -H (**) (* destruct: the destucted equality is not erased *)
+  /2 width=1/
+]
+qed-.
+
+(* Basic properties *********************************************************)
+
+(* Basic_1: was: term_dec *)
+axiom term_eq_dec: ∀T1,T2:term. Decidable (T1 = T2).
+
+(* Basic_1: removed theorems 3:
+            not_void_abst not_abbr_void not_abst_void
+*)