| 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 "global reference (term)" 'GRef p = (TAtom (GRef p)).
+interpretation "term binding construction (binary)"
+ 'SnBind2 I T1 T2 = (TPair (Bind2 I) T1 T2).
-interpretation "term construction (atomic)" 'SItem I = (TAtom I).
+interpretation "term flat construction (binary)"
+ 'SnFlat2 I T1 T2 = (TPair (Flat2 I) T1 T2).
-interpretation "term construction (binary)" 'SItem I T1 T2 = (TPair I T1 T2).
+interpretation "sort (term)"
+ 'Star k = (TAtom (Sort k)).
-interpretation "term binding construction (binary)" 'SBind I T1 T2 = (TPair (Bind I) T1 T2).
+interpretation "local reference (term)"
+ 'LRef i = (TAtom (LRef i)).
-interpretation "term flat construction (binary)" 'SFlat I T1 T2 = (TPair (Flat I) T1 T2).
+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. 𝕔{I} V. T = V → False.
+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
-(*
- (generalize in match e1) -e1 >e0 normalize
-*) -I /2/ (**) (* destruct: one quality is not simplified, the destucted equality is not erased *)
+ -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. 𝕔{I} V. T = T → False.
+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 -I V /2/ (**) (* destruct: the destucted equality is not erased *)
+| #J #W #U #_ #IHU #H destruct
+ -H (**) (* destruct: the destucted equality is not erased *)
+ /2 width=1/
]
qed-.