X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flsubr.ma;h=352626ccd8f4d7051afad29b3a8117b6a357e7ad;hb=fed8c1a61273b0eb4a719fda70e2b5dd31933c8a;hp=111da17511225ed78d90f289af41e88278639910;hpb=43282d3750af8831c8100c60d75c56fdfb7ff3c9;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
index 111da1751..352626ccd 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
@@ -13,9 +13,9 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lrsubeqc_2.ma".
-include "basic_2/substitution/drop.ma".
+include "basic_2/syntax/lenv.ma".
 
-(* RESTRICTED LOCAL ENVIRONMENT REFINEMENT **********************************)
+(* RESTRICTED REFINEMENT FOR LOCAL ENVIRONMENTS *****************************)
 
 inductive lsubr: relation lenv ≝
 | lsubr_atom: ∀L. lsubr L (⋆)
@@ -24,7 +24,7 @@ inductive lsubr: relation lenv ≝
 .
 
 interpretation
-  "local environment refinement (restricted)"
+  "restricted refinement (local environment)"
   'LRSubEqC L1 L2 = (lsubr L1 L2).
 
 (* Basic properties *********************************************************)
@@ -58,50 +58,46 @@ lemma lsubr_inv_abst1: ∀K1,L2,W. K1.ⓛW ⫃ L2 →
                        L2 = ⋆ ∨ ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓛW.
 /2 width=3 by lsubr_inv_abst1_aux/ qed-.
 
-fact lsubr_inv_abbr2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,W. L2 = K2.ⓓW →
-                          ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓW.
+fact lsubr_inv_pair2_aux: ∀L1,L2. L1 ⫃ L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
+                          (∃∃K1. K1 ⫃ K2 & L1 = K1.ⓑ{I}W) ∨
+                          ∃∃K1,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V & I = Abst.
 #L1 #L2 * -L1 -L2
-[ #L #K2 #W #H destruct
-| #I #L1 #L2 #V #HL12 #K2 #W #H destruct /2 width=3 by ex2_intro/
-| #L1 #L2 #V1 #V2 #_ #K2 #W #H destruct
+[ #L #J #K2 #W #H destruct
+| #I #L1 #L2 #V #HL12 #J #K2 #W #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #V1 #V2 #HL12 #J #K2 #W #H destruct /3 width=4 by ex3_2_intro, or_intror/
 ]
 qed-.
 
-lemma lsubr_inv_abbr2: ∀L1,K2,W. L1 ⫃ K2.ⓓW →
-                       ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓW.
-/2 width=3 by lsubr_inv_abbr2_aux/ qed-.
+lemma lsubr_inv_pair2: ∀I,L1,K2,W. L1 ⫃ K2.ⓑ{I}W →
+                       (∃∃K1. K1 ⫃ K2 & L1 = K1.ⓑ{I}W) ∨
+                       ∃∃K1,V1. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V1 & I = Abst.
+/2 width=3 by lsubr_inv_pair2_aux/ qed-.
 
-(* Basic forward lemmas *****************************************************)
+(* Advanced inversion lemmas ************************************************)
 
-lemma lsubr_fwd_length: ∀L1,L2. L1 ⫃ L2 → |L2| ≤ |L1|.
-#L1 #L2 #H elim H -L1 -L2 /2 width=1 by monotonic_le_plus_l/
+lemma lsubr_inv_abbr2: ∀L1,K2,V. L1 ⫃ K2.ⓓV →
+                       ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓV.
+#L1 #K2 #V #H elim (lsubr_inv_pair2 … H) -H *
+[ #K1 #HK12 #H destruct /2 width=3 by ex2_intro/
+| #K1 #V1 #_ #_ #H destruct
+]
 qed-.
 
-lemma lsubr_fwd_drop2_pair: ∀L1,L2. L1 ⫃ L2 →
-                            ∀I,K2,W,s,i. ⬇[s, 0, i] L2 ≡ K2.ⓑ{I}W →
-                            (∃∃K1. K1 ⫃ K2 & ⬇[s, 0, i] L1 ≡ K1.ⓑ{I}W) ∨
-                            ∃∃K1,V. K1 ⫃ K2 & ⬇[s, 0, i] L1 ≡ K1.ⓓⓝW.V & I = Abst.
-#L1 #L2 #H elim H -L1 -L2
-[ #L #I #K2 #W #s #i #H
-  elim (drop_inv_atom1 … H) -H #H destruct
-| #J #L1 #L2 #V #HL12 #IHL12 #I #K2 #W #s #i #H
-  elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
-  [ /3 width=3 by drop_pair, ex2_intro, or_introl/
-  | elim (IHL12 … HLK2) -IHL12 -HLK2 *
-    /4 width=4 by drop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
-  ]
-| #L1 #L2 #V1 #V2 #HL12 #IHL12 #I #K2 #W #s #i #H
-  elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
-  [ /3 width=4 by drop_pair, ex3_2_intro, or_intror/
-  | elim (IHL12 … HLK2) -IHL12 -HLK2 *
-    /4 width=4 by drop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
-  ]
+lemma lsubr_inv_abst2: ∀L1,K2,W. L1 ⫃ K2.ⓛW →
+                       (∃∃K1. K1 ⫃ K2 & L1 = K1.ⓛW) ∨
+                       ∃∃K1,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V.
+#L1 #K2 #W #H elim (lsubr_inv_pair2 … H) -H *
+[ #K1 #HK12 #H destruct /3 width=3 by ex2_intro, or_introl/
+| #K1 #V1 #HK12 #H #_ destruct /3 width=4 by ex2_2_intro, or_intror/
 ]
 qed-.
 
-lemma lsubr_fwd_drop2_abbr: ∀L1,L2. L1 ⫃ L2 →
-                            ∀K2,V,s,i. ⬇[s, 0, i] L2 ≡ K2.ⓓV →
-                            ∃∃K1. K1 ⫃ K2 & ⬇[s, 0, i] L1 ≡ K1.ⓓV.
-#L1 #L2 #HL12 #K2 #V #s #i #HLK2 elim (lsubr_fwd_drop2_pair … HL12 … HLK2) -L2 // *
-#K1 #W #_ #_ #H destruct
+(* Basic forward lemmas *****************************************************)
+
+lemma lsubr_fwd_pair2: ∀I2,L1,K2,V2. L1 ⫃ K2.ⓑ{I2}V2 →
+                       ∃∃I1,K1,V1. K1 ⫃ K2 & L1 = K1.ⓑ{I1}V1.
+#I2 #L1 #K2 #V2 #H elim (lsubr_inv_pair2 … H) -H *
+[ #K1 #HK12 #H destruct /3 width=5 by ex2_3_intro/
+| #K1 #V1 #HK12 #H1 #H2 destruct /3 width=5 by ex2_3_intro/
+]
 qed-.