- update in Basic_2

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / grammar / term.ma

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 376061b70bb52cef59e3b11c08cb920ab6ba42ff..6e8370d497251de2cfd69bfba097e5418823bb77 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/grammar/term.ma
@@ -22,44 +22,95 @@ 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 "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 properties *********************************************************)
+
+(* Basic_1: was: term_dec *)
+axiom term_eq_dec: ∀T1,T2:term. Decidable (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-.
 
-(* Basic properties *********************************************************)
+lemma eq_false_inv_tpair_sn: ∀I,V1,T1,V2,T2.
+                             (②{I} V1. T1 = ②{I} V2. T2 → False) →
+                             (V1 = V2 → False) ∨ (V1 = V2 ∧ (T1 = T2 → False)).
+#I #V1 #T1 #V2 #T2 #H
+elim (term_eq_dec V1 V2) /3 width=1/ #HV12 destruct
+@or_intror @conj // #HT12 destruct /2 width=1/ 
+qed-.
 
-(* Basic_1: was: term_dec *)
-axiom term_eq_dec: ∀T1,T2:term. Decidable (T1 = T2).
+lemma eq_false_inv_tpair_dx: ∀I,V1,T1,V2,T2.
+                             (②{I} V1. T1 = ②{I} V2. T2 → False) →
+                             (T1 = T2 → False) ∨ (T1 = T2 ∧ (V1 = V2 → False)).
+#I #V1 #T1 #V2 #T2 #H
+elim (term_eq_dec T1 T2) /3 width=1/ #HT12 destruct
+@or_intror @conj // #HT12 destruct /2 width=1/
+qed-.
+
+lemma eq_false_inv_beta: ∀V1,V2,W1,W2,T1,T2.
+                         (ⓐV1. ⓛW1. T1 = ⓐV2. ⓛW2 .T2 →False) →
+                         (W1 = W2 → False) ∨
+                         (W1 = W2 ∧ (ⓓV1. T1 = ⓓV2. T2 → False)).
+#V1 #V2 #W1 #W2 #T1 #T2 #H
+elim (eq_false_inv_tpair_sn … H) -H
+[ #HV12 elim (term_eq_dec W1 W2) /3 width=1/
+  #H destruct @or_intror @conj // #H destruct /2 width=1/
+| * #H1 #H2 destruct
+  elim (eq_false_inv_tpair_sn … H2) -H2 /3 width=1/
+  * #H #HT12 destruct
+  @or_intror @conj // #H destruct /2 width=1/
+]
+qed.
 
 (* Basic_1: removed theorems 3:
             not_void_abst not_abbr_void not_abst_void