milestone update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / syntax / term.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/syntax/term.ma b/matita/matita/contribs/lambdadelta/static_2/syntax/term.ma
index 83937e544226be06d98f104f1ba78a054d19d80e..0a6f97872a2e199d22d582cc0b087b8edadae198 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/syntax/term.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/syntax/term.ma
@@ -36,72 +36,91 @@ include "static_2/syntax/item.ma".
 
 (* terms *)
 inductive term: Type[0] ≝
-  | TAtom: item0 → term               (* atomic item construction *)
-  | TPair: item2 → term → term → term (* binary item construction *)
+| TAtom: item0 → term               (* atomic item construction *)
+| TPair: item2 → term → term → term (* binary item construction *)
 .
 
-interpretation "term construction (atomic)"
-   'Item0 I = (TAtom I).
+interpretation
+  "term construction (atomic)"
+  'Item0 I = (TAtom I).
 
-interpretation "term construction (binary)"
-   'SnItem2 I T1 T2 = (TPair I T1 T2).
+interpretation
+  "term construction (binary)"
+  'SnItem2 I T1 T2 = (TPair I T1 T2).
 
-interpretation "term binding construction (binary)"
-   'SnBind2 p I T1 T2 = (TPair (Bind2 p I) T1 T2).
+interpretation
+   "term binding construction (binary)"
+  'SnBind2 p I T1 T2 = (TPair (Bind2 p I) T1 T2).
 
-interpretation "term positive binding construction (binary)"
-   'SnBind2Pos I T1 T2 = (TPair (Bind2 true I) T1 T2).
+interpretation
+  "term positive binding construction (binary)"
+  'SnBind2Pos I T1 T2 = (TPair (Bind2 true I) T1 T2).
 
-interpretation "term negative binding construction (binary)"
-   'SnBind2Neg I T1 T2 = (TPair (Bind2 false I) T1 T2).
+interpretation
+  "term negative binding construction (binary)"
+  'SnBind2Neg I T1 T2 = (TPair (Bind2 false I) T1 T2).
 
-interpretation "term flat construction (binary)"
-   'SnFlat2 I T1 T2 = (TPair (Flat2 I) T1 T2).
+interpretation
+  "term flat construction (binary)"
+  'SnFlat2 I T1 T2 = (TPair (Flat2 I) T1 T2).
 
-interpretation "sort (term)"
-   'Star s = (TAtom (Sort s)).
+interpretation
+  "sort (term)"
+  'Star s = (TAtom (Sort s)).
 
-interpretation "local reference (term)"
-   'LRef i = (TAtom (LRef i)).
+interpretation
+  "local reference (term)"
+  'LRef i = (TAtom (LRef i)).
 
-interpretation "global reference (term)"
-   'GRef l = (TAtom (GRef l)).
+interpretation
+  "global reference (term)"
+  'GRef l = (TAtom (GRef l)).
 
-interpretation "abbreviation (term)"
-   'SnAbbr p T1 T2 = (TPair (Bind2 p Abbr) T1 T2).
+interpretation
+  "abbreviation (term)"
+  'SnAbbr p T1 T2 = (TPair (Bind2 p Abbr) T1 T2).
 
-interpretation "positive abbreviation (term)"
-   'SnAbbrPos T1 T2 = (TPair (Bind2 true Abbr) T1 T2).
+interpretation
+  "positive abbreviation (term)"
+  'SnAbbrPos T1 T2 = (TPair (Bind2 true Abbr) T1 T2).
 
-interpretation "negative abbreviation (term)"
-   'SnAbbrNeg T1 T2 = (TPair (Bind2 false Abbr) T1 T2).
+interpretation
+  "negative abbreviation (term)"
+  'SnAbbrNeg T1 T2 = (TPair (Bind2 false Abbr) T1 T2).
 
-interpretation "abstraction (term)"
-   'SnAbst p T1 T2 = (TPair (Bind2 p Abst) T1 T2).
+interpretation
+  "abstraction (term)"
+  'SnAbst p T1 T2 = (TPair (Bind2 p Abst) T1 T2).
 
-interpretation "positive abstraction (term)"
-   'SnAbstPos T1 T2 = (TPair (Bind2 true Abst) T1 T2).
+interpretation
+  "positive abstraction (term)"
+  'SnAbstPos T1 T2 = (TPair (Bind2 true Abst) T1 T2).
 
-interpretation "negative abstraction (term)"
-   'SnAbstNeg T1 T2 = (TPair (Bind2 false Abst) T1 T2).
+interpretation
+  "negative abstraction (term)"
+  'SnAbstNeg T1 T2 = (TPair (Bind2 false Abst) T1 T2).
 
-interpretation "application (term)"
-   'SnAppl T1 T2 = (TPair (Flat2 Appl) 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).
+interpretation
+  "native type annotation (term)"
+  'SnCast T1 T2 = (TPair (Flat2 Cast) T1 T2).
 
 (* Basic properties *********************************************************)
 
-lemma abst_dec (X): ∨∨ ∃∃p,W,T. X = ⓛ[p]W.T
-                     | (∀p,W,T. X = ⓛ[p]W.T → ⊥).
+lemma abst_dec (X):
+      ∨∨ ∃∃p,W,T. X = ⓛ[p]W.T
+       | (∀p,W,T. X = ⓛ[p]W.T → ⊥).
 * [ #I | * [ #p * | #I ] #V #T ]
 [3: /3 width=4 by ex1_3_intro, or_introl/ ]
 @or_intror #q #W #U #H destruct
 qed-.
 
 (* Basic_1: was: term_dec *)
-lemma eq_term_dec: ∀T1,T2:term. Decidable (T1 = T2).
+lemma eq_term_dec:
+      ∀T1,T2:term. Decidable (T1 = T2).
 #T1 elim T1 -T1 #I1 [| #V1 #T1 #IHV1 #IHT1 ] * #I2 [2,4: #V2 #T2 ]
 [1,4: @or_intror #H destruct
 | elim (eq_item2_dec I1 I2) #HI
@@ -116,16 +135,19 @@ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact destruct_tatom_tatom_aux: ∀I1,I2. ⓪[I1] = ⓪[I2] → I1 = I2.
+fact destruct_tatom_tatom_aux:
+     ∀I1,I2. ⓪[I1] = ⓪[I2] → I1 = I2.
 #I1 #I2 #H destruct //
 qed-.
 
-fact destruct_tpair_tpair_aux: ∀I1,I2,T1,T2,V1,V2. ②[I1]T1.V1 = ②[I2]T2.V2 →
-                               ∧∧T1 = T2 & I1 = I2 & V1 = V2.
+fact destruct_tpair_tpair_aux:
+     ∀I1,I2,T1,T2,V1,V2. ②[I1]T1.V1 = ②[I2]T2.V2 →
+     ∧∧ T1 = T2 & I1 = I2 & V1 = V2.
 #I1 #I2 #T1 #T2 #V1 #V2 #H destruct /2 width=1 by and3_intro/
 qed-.
 
-lemma discr_tpair_xy_x: ∀I,T,V. ②[I]V.T = V → ⊥.
+lemma discr_tpair_xy_x:
+      ∀I,T,V. ②[I]V.T = V → ⊥.
 #I #T #V elim V -V
 [ #J #H destruct
 | #J #W #U #IHW #_ #H elim (destruct_tpair_tpair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
@@ -133,24 +155,27 @@ lemma discr_tpair_xy_x: ∀I,T,V. ②[I]V.T = V → ⊥.
 qed-.
 
 (* Basic_1: was: thead_x_y_y *)
-lemma discr_tpair_xy_y: ∀I,V,T. ②[I]V.T = T → ⊥.
+lemma discr_tpair_xy_y:
+      ∀I,V,T. ②[I]V.T = T → ⊥.
 #I #V #T elim T -T
 [ #J #H destruct
 | #J #W #U #_ #IHU #H elim (destruct_tpair_tpair_aux … H) -H /2 width=1 by/ (**) (* destruct lemma needed *)
 ]
 qed-.
 
-lemma eq_false_inv_tpair_sn: ∀I,V1,T1,V2,T2.
-                             (②[I]V1.T1 = ②[I]V2.T2 → ⊥) →
-                             (V1 = V2 → ⊥) ∨ (V1 = V2 ∧ (T1 = T2 → ⊥)).
+lemma eq_false_inv_tpair_sn:
+      ∀I,V1,T1,V2,T2.
+      (②[I]V1.T1 = ②[I]V2.T2 → ⊥) →
+      (V1 = V2 → ⊥) ∨ (V1 = V2 ∧ (T1 = T2 → ⊥)).
 #I #V1 #T1 #V2 #T2 #H
 elim (eq_term_dec V1 V2) /3 width=1 by or_introl/ #HV12 destruct
 @or_intror @conj // #HT12 destruct /2 width=1 by/
 qed-.
 
-lemma eq_false_inv_tpair_dx: ∀I,V1,T1,V2,T2.
-                             (②[I] V1. T1 = ②[I]V2.T2 → ⊥) →
-                             (T1 = T2 → ⊥) ∨ (T1 = T2 ∧ (V1 = V2 → ⊥)).
+lemma eq_false_inv_tpair_dx:
+      ∀I,V1,T1,V2,T2.
+      (②[I] V1. T1 = ②[I]V2.T2 → ⊥) →
+      (T1 = T2 → ⊥) ∨ (T1 = T2 ∧ (V1 = V2 → ⊥)).
 #I #V1 #T1 #V2 #T2 #H
 elim (eq_term_dec T1 T2) /3 width=1 by or_introl/ #HT12 destruct
 @or_intror @conj // #HT12 destruct /2 width=1 by/