From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Tue, 17 Oct 2017 15:24:43 +0000 (+0000)
Subject: - exclusion binder in local environments
X-Git-Tag: make_still_working~433
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=0098ddc7269a3fc4a554cf386d2a234d61d53d44;p=helm.git

- exclusion binder in local environments
  component i_static updated
  (this is part of last milestone)
---

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc
index e2f613a87..8e7e11183 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/tc_lfxs.etc
@@ -39,6 +39,21 @@ axiom s_r_conf2_LTC2: ∀R. s_r_transitive … R (lfxs R) →
 #L1 #L #HL1 #HL2 #IH @(tc_lfxs_step_sn … IH) -IH //
 *)
 
+lemma tc_lfxs_inv_zero: ∀R,Y1,Y2. Y1 ⪤**[R, #0] Y2 →
+                        ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
+                         | ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, V1] L2 & R L1 V1 V2 &
+                                            Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2
+                         | ∃∃f,I,L1,L2. 𝐈⦃f⦄ & L1 ⪤*[cext2 R, cfull, f] L2 &
+                                        Y1 = L1.ⓤ{I} & Y2 = L2.ⓤ{I}.
+#R #Y1 #Y2 #H elim H -Y2
+[
+| #Y #Y2 #_ #H elim (lfxs_inv_zero … H) -H *
+  [ #H #H2 * * /3 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex4_4_intro, conj/
+  | #I #L #L2 #V #V2 #HL2 #HV2 #H #H2 * *
+    [ #H1 #H0 destruct
+    | #I0 #L0 #L1 #V0 #V1 #HL01 #HV01 #H1 #H0 destruct  
+
+
 lemma tc_lfxs_inv_zero: ∀R. s_r_confluent1 … R (lfxs R) →
                         s_r_transitive … R (lfxs R) →
                         ∀Y1,Y2. Y1 ⦻**[R, #0] Y2 →
diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma
index e1dd22673..8e3bf8a4d 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma
@@ -44,13 +44,17 @@ lemma tc_lfxs_sort: ∀R,I,L1,L2,V1,V2,s.
 /3 width=4 by lfxs_sort, tc_lfxs_step_dx, inj/
 qed.
 
-lemma tc_lfxs_zero: ∀R. (∀L. reflexive … (R L)) →
+lemma tc_lfxs_pair: ∀R. (∀L. reflexive … (R L)) →
                     ∀I,L1,L2,V. L1 ⪤**[R, V] L2 →
                     L1.ⓑ{I}V ⪤**[R, #0] L2.ⓑ{I}V.
 #R #HR #I #L1 #L2 #V #H elim H -L2
-/3 width=5 by lfxs_zero, tc_lfxs_step_dx, inj/
+/3 width=5 by lfxs_pair, tc_lfxs_step_dx, inj/
 qed.
 
+lemma tc_lfxs_unit: ∀R,f,I,L1,L2. 𝐈⦃f⦄ → L1 ⪤*[cext2 R, cfull, f] L2 →
+                    L1.ⓤ{I} ⪤**[R, #0] L2.ⓤ{I}.
+/3 width=3 by lfxs_unit, inj/ qed.
+
 lemma tc_lfxs_lref: ∀R,I,L1,L2,V1,V2,i.
                     L1 ⪤**[R, #i] L2 → L1.ⓑ{I}V1 ⪤**[R, #⫯i] L2.ⓑ{I}V2.
 #R #I #L1 #L2 #V1 #V2 #i #H elim H -L2
@@ -63,7 +67,7 @@ lemma tc_lfxs_gref: ∀R,I,L1,L2,V1,V2,l.
 /3 width=4 by lfxs_gref, tc_lfxs_step_dx, inj/
 qed.
 
-lemma tc_lfxs_sym: ∀R. lexs_frees_confluent R cfull →
+lemma tc_lfxs_sym: ∀R. lexs_frees_confluent (cext2 R) cfull →
                    (∀L1,L2,T1,T2. R L1 T1 T2 → R L2 T2 T1) →
                    ∀T. symmetric … (tc_lfxs R T).
 #R #H1R #H2R #T #L1 #L2 #H elim H -L2
@@ -90,36 +94,36 @@ lemma tc_lfxs_inv_atom_dx: ∀R,I,Y1. Y1 ⪤**[R, ⓪{I}] ⋆ → Y1 = ⋆.
 qed-.
 
 lemma tc_lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⪤**[R, ⋆s] Y2 →
-                        (Y1 = ⋆ ∧ Y2 = ⋆) ∨
-                        ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, ⋆s] L2 &
-                                         Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
+                        ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
+                         | ∃∃I1,I2,L1,L2. L1 ⪤**[R, ⋆s] L2 &
+                                          Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
 #R #Y1 #Y2 #s #H elim H -Y2
 [ #Y2 #H elim (lfxs_inv_sort … H) -H *
-  /4 width=8 by ex3_5_intro, inj, or_introl, or_intror, conj/
+  /4 width=8 by ex3_4_intro, inj, or_introl, or_intror, conj/
 | #Y #Y2 #_ #H elim (lfxs_inv_sort … H) -H *
-  [ #H #H2 * * /3 width=8 by ex3_5_intro, or_introl, or_intror, conj/
-  | #I #L #L2 #V #V2 #HL2 #H #H2 * *
+  [ #H #H2 * * /3 width=7 by ex3_4_intro, or_introl, or_intror, conj/
+  | #I #I2 #L #L2 #HL2 #H #H2 * *
     [ #H1 #H0 destruct
-    | #I0 #L1 #L0 #V1 #V0 #HL10 #H1 #H0 destruct
-      /4 width=8 by ex3_5_intro, tc_lfxs_step_dx, or_intror/
+    | #I1 #I0 #L1 #L0 #HL10 #H1 #H0 destruct
+      /4 width=7 by ex3_4_intro, tc_lfxs_step_dx, or_intror/
     ]
   ]
 ] 
 qed-.
 
 lemma tc_lfxs_inv_gref: ∀R,Y1,Y2,l. Y1 ⪤**[R, §l] Y2 →
-                        (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
-                        ∃∃I,L1,L2,V1,V2. L1 ⪤**[R, §l] L2 &
-                                         Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
+                        ∨∨ Y1 = ⋆ ∧ Y2 = ⋆
+                         | ∃∃I1,I2,L1,L2. L1 ⪤**[R, §l] L2 &
+                                          Y1 = L1.ⓘ{I1} & Y2 = L2.ⓘ{I2}.
 #R #Y1 #Y2 #l #H elim H -Y2
 [ #Y2 #H elim (lfxs_inv_gref … H) -H *
-  /4 width=8 by ex3_5_intro, inj, or_introl, or_intror, conj/
+  /4 width=8 by ex3_4_intro, inj, or_introl, or_intror, conj/
 | #Y #Y2 #_ #H elim (lfxs_inv_gref … H) -H *
-  [ #H #H2 * * /3 width=8 by ex3_5_intro, or_introl, or_intror, conj/
-  | #I #L #L2 #V #V2 #HL2 #H #H2 * *
+  [ #H #H2 * * /3 width=7 by ex3_4_intro, or_introl, or_intror, conj/
+  | #I #I2 #L #L2 #HL2 #H #H2 * *
     [ #H1 #H0 destruct
-    | #I0 #L1 #L0 #V1 #V0 #HL10 #H1 #H0 destruct
-      /4 width=8 by ex3_5_intro, tc_lfxs_step_dx, or_intror/
+    | #I1 #I0 #L1 #L0 #HL10 #H1 #H0 destruct
+      /4 width=7 by ex3_4_intro, tc_lfxs_step_dx, or_intror/
     ]
   ]
 ] 
@@ -144,35 +148,35 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma tc_lfxs_inv_sort_pair_sn: ∀R,I,Y2,L1,V1,s. L1.ⓑ{I}V1 ⪤**[R, ⋆s] Y2 →
-                                ∃∃L2,V2. L1 ⪤**[R, ⋆s] L2 & Y2 = L2.ⓑ{I}V2.
-#R #I #Y2 #L1 #V1 #s #H elim (tc_lfxs_inv_sort … H) -H *
+lemma tc_lfxs_inv_sort_bind_sn: ∀R,I1,Y2,L1,s. L1.ⓘ{I1} ⪤**[R, ⋆s] Y2 →
+                                ∃∃I2,L2. L1 ⪤**[R, ⋆s] L2 & Y2 = L2.ⓘ{I2}.
+#R #I1 #Y2 #L1 #s #H elim (tc_lfxs_inv_sort … H) -H *
 [ #H destruct
-| #J #Y1 #L2 #X1 #V2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
+| #Z #I2 #Y1 #L2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma tc_lfxs_inv_sort_pair_dx: ∀R,I,Y1,L2,V2,s. Y1 ⪤**[R, ⋆s] L2.ⓑ{I}V2 →
-                                ∃∃L1,V1. L1 ⪤**[R, ⋆s] L2 & Y1 = L1.ⓑ{I}V1.
-#R #I #Y1 #L2 #V2 #s #H elim (tc_lfxs_inv_sort … H) -H *
+lemma tc_lfxs_inv_sort_bind_dx: ∀R,I2,Y1,L2,s. Y1 ⪤**[R, ⋆s] L2.ⓘ{I2} →
+                                ∃∃I1,L1. L1 ⪤**[R, ⋆s] L2 & Y1 = L1.ⓘ{I1}.
+#R #I2 #Y1 #L2 #s #H elim (tc_lfxs_inv_sort … H) -H *
 [ #_ #H destruct
-| #J #L1 #Y2 #V1 #X2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
+| #I1 #Z #L1 #Y2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma tc_lfxs_inv_gref_pair_sn: ∀R,I,Y2,L1,V1,l. L1.ⓑ{I}V1 ⪤**[R, §l] Y2 →
-                                ∃∃L2,V2. L1 ⪤**[R, §l] L2 & Y2 = L2.ⓑ{I}V2.
-#R #I #Y2 #L1 #V1 #l #H elim (tc_lfxs_inv_gref … H) -H *
+lemma tc_lfxs_inv_gref_bind_sn: ∀R,I1,Y2,L1,l. L1.ⓘ{I1} ⪤**[R, §l] Y2 →
+                                ∃∃I2,L2. L1 ⪤**[R, §l] L2 & Y2 = L2.ⓘ{I2}.
+#R #I1 #Y2 #L1 #l #H elim (tc_lfxs_inv_gref … H) -H *
 [ #H destruct
-| #J #Y1 #L2 #X1 #V2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
+| #Z #I2 #Y1 #L2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma tc_lfxs_inv_gref_pair_dx: ∀R,I,Y1,L2,V2,l. Y1 ⪤**[R, §l] L2.ⓑ{I}V2 →
-                                ∃∃L1,V1. L1 ⪤**[R, §l] L2 & Y1 = L1.ⓑ{I}V1.
-#R #I #Y1 #L2 #V2 #l #H elim (tc_lfxs_inv_gref … H) -H *
+lemma tc_lfxs_inv_gref_bind_dx: ∀R,I2,Y1,L2,l. Y1 ⪤**[R, §l] L2.ⓘ{I2} →
+                                ∃∃I1,L1. L1 ⪤**[R, §l] L2 & Y1 = L1.ⓘ{I1}.
+#R #I2 #Y1 #L2 #l #H elim (tc_lfxs_inv_gref … H) -H *
 [ #_ #H destruct
-| #J #L1 #Y2 #V1 #X2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
+| #I1 #Z #L1 #Y2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma
index e69f071f2..ce56a3154 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma
@@ -46,3 +46,22 @@ lemma tc_lfxs_ind_dx: ∀R. (∀L. reflexive … (R L)) →
 #R #HR #L2 #R0 #HL2 #IHL2 #L1 #HL12
 @(TC_star_ind_dx … HL2 IHL2 … HL12) /2 width=4 by lfxs_refl/
 qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma tc_lfxs_inv_bind_void: ∀R. (∀L. reflexive … (R L)) →
+                             ∀p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 →
+                             L1 ⪤**[R, V] L2 ∧ L1.ⓧ ⪤**[R, T] L2.ⓧ.
+#R #HR #p #I #L1 #L2 #V #T #H @(tc_lfxs_ind_sn … HR … H) -L2
+[ /3 width=1 by tc_lfxs_refl, conj/
+| #L #L2 #_ #H * elim (lfxs_inv_bind_void … H) -H /3 width=3 by tc_lfxs_step_dx, conj/
+]
+qed-.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma tc_lfxs_fwd_bind_dx_void: ∀R. (∀L. reflexive … (R L)) →
+                                ∀p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 →
+                                L1.ⓧ ⪤**[R, T] L2.ⓧ.
+#R #HR #p #I #L1 #L2 #V #T #H elim (tc_lfxs_inv_bind_void … H) -H //
+qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma
index 4fe37f452..62173d926 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_tc_lfxs.ma
@@ -19,5 +19,5 @@ include "basic_2/i_static/tc_lfxs.ma".
 (* Main properties **********************************************************)
 
 theorem tc_lfxs_trans: ∀R,T. Transitive … (tc_lfxs R T).
-#R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *) 
+#R #T #L1 #L #HL1 #L2 #HL2 @(trans_TC … HL1 HL2) (**) (* auto fails *)
 qed-.
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
index 74819fc02..dcf2f4693 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
@@ -34,9 +34,10 @@
 
    <subsection name="A2">Stage "A2": "Extending the Applicability Condition"</subsection>
 
-   <news class="alpha" date="2017 October 16.">
+   <news class="alpha" date="2017 October 17.">
          Exclusion binder in local environments.
-         Ported components: syntax, relocation, s_transition, s_computation, static.
+         Syntactic component updated:
+         syntax, relocation, s_transition, s_computation, static, i_static.
    </news>
    <news class="alpha" date="2017 April 16.">
          Strong rt-normalization
diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 059745fe9..df82586f0 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -148,6 +148,7 @@ table {
         ]
      }
    ]
+*)
    class "water"
    [ { "iterated static typing" * } {
         [ { "iterated extension on referred entries" * } {
@@ -156,7 +157,6 @@ table {
         ]
      }
    ]
-*)
    class "green"
    [ { "static typing" * } {
         [ { "generic reducibility" * } {