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 -I /2/ (**) (* improve context after 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.
+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/ (**) (* improve context after destruct *)
+| #J #W #U #_ #IHU #H destruct
+ -H (**) (* destruct: the destucted equality is not erased *)
+ /2 width=1/
]
-qed.
+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
+*)