interpretation "term binding construction (binary)" 'SBind I T1 T2 = (TPair (Bind I) T1 T2).
interpretation "term flat construction (binary)" 'SFlat I T1 T2 = (TPair (Flat I) T1 T2).
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma discr_tpair_xy_x: ∀I,T,V. 𝕔{I} V. T = V → False.
+#I #T #V elim V -V
+[ #J #H destruct
+| #J #W #U #IHW #_ #H destruct
+(*
+ (generalize in match e1) -e1 >e0 normalize
+*) -I /2/ (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
+]
+qed-.
+
+(* Basic_1: was: thead_x_y_y *)
+lemma discr_tpair_xy_y: ∀I,V,T. 𝕔{I} V. T = T → False.
+#I #V #T elim T -T
+[ #J #H destruct
+| #J #W #U #_ #IHU #H destruct -I V /2/ (**) (* destruct: the destucted equality is not erased *)
+]
+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
+*)