- partial commit of rt_transition ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsubr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
index ea1ddabecb8368b4866de471946c0f48d2f089e8..c4ec6dd188e36c6eeca2148debbfd0d9380e00c4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
@@ -13,24 +13,24 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lrsubeqc_2.ma".
-include "basic_2/substitution/ldrop.ma".
+include "basic_2/grammar/lenv.ma".
 
-(* RESTRICTED LOCAL ENVIRONMENT REFINEMENT **********************************)
+(* RESTRICTED REFINEMENT FOR LOCAL ENVIRONMENTS *****************************)
 
 inductive lsubr: relation lenv ≝
-| lsubr_sort: ∀L. lsubr L (⋆)
-| lsubr_bind: ∀I,L1,L2,V. lsubr L1 L2 → lsubr (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsubr_abst: ∀L1,L2,V,W. lsubr L1 L2 → lsubr (L1.ⓓⓝW.V) (L2.ⓛW)
+| lsubr_atom: ∀L. lsubr L (⋆)
+| lsubr_pair: ∀I,L1,L2,V. lsubr L1 L2 → lsubr (L1.ⓑ{I}V) (L2.ⓑ{I}V)
+| lsubr_beta: ∀L1,L2,V,W. lsubr L1 L2 → lsubr (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
 interpretation
-  "local environment refinement (restricted)"
+  "restricted refinement (local environment)"
   'LRSubEqC L1 L2 = (lsubr L1 L2).
 
 (* Basic properties *********************************************************)
 
 lemma lsubr_refl: ∀L. L ⫃ L.
-#L elim L -L /2 width=1 by lsubr_sort, lsubr_bind/
+#L elim L -L /2 width=1 by lsubr_atom, lsubr_pair/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -58,8 +58,8 @@ 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_abbr2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,V. L2 = K2.ⓓV →
+                          ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓV.
 #L1 #L2 * -L1 -L2
 [ #L #K2 #W #H destruct
 | #I #L1 #L2 #V #HL12 #K2 #W #H destruct /2 width=3 by ex2_intro/
@@ -67,41 +67,30 @@ fact lsubr_inv_abbr2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,W. L2 = K2.ⓓW →
 ]
 qed-.
 
-lemma lsubr_inv_abbr2: ∀L1,K2,W. L1 ⫃ K2.ⓓW →
-                       ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓW.
+lemma lsubr_inv_abbr2: ∀L1,K2,V. L1 ⫃ K2.ⓓV →
+                       ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓV.
 /2 width=3 by lsubr_inv_abbr2_aux/ qed-.
 
-(* Basic forward 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/
-qed-.
-
-lemma lsubr_fwd_ldrop2_bind: ∀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 (ldrop_inv_atom1 … H) -H #H destruct
-| #J #L1 #L2 #V #HL12 #IHL12 #I #K2 #W #s #i #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
-  [ /3 width=3 by ldrop_pair, ex2_intro, or_introl/
-  | elim (IHL12 … HLK2) -IHL12 -HLK2 *
-    /4 width=4 by ldrop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
-  ]
-| #L1 #L2 #V1 #V2 #HL12 #IHL12 #I #K2 #W #s #i #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #Hi #HLK2 destruct [ -IHL12 | -HL12 ]
-  [ /3 width=4 by ldrop_pair, ex3_2_intro, or_intror/
-  | elim (IHL12 … HLK2) -IHL12 -HLK2 *
-    /4 width=4 by ldrop_drop_lt, ex3_2_intro, ex2_intro, or_introl, or_intror/
-  ]
+fact lsubr_inv_abst2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,W. L2 = K2.ⓛW →
+                          (∃∃K1. K1 ⫃ K2 & L1 = K1.ⓛW) ∨
+                          ∃∃K1,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V.
+#L1 #L2 * -L1 -L2
+[ #L #K2 #W #H destruct
+| #I #L1 #L2 #V #HL12 #K2 #W #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #V1 #V2 #HL12 #K2 #W #H destruct /3 width=4 by ex2_2_intro, or_intror/
 ]
 qed-.
 
-lemma lsubr_fwd_ldrop2_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_ldrop2_bind … HL12 … HLK2) -L2 // *
-#K1 #W #_ #_ #H destruct
+lemma lsubr_inv_abst2: ∀L1,K2,W. L1 ⫃ K2.ⓛW →
+                       (∃∃K1. K1 ⫃ K2 & L1 = K1.ⓛW) ∨
+                       ∃∃K1,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V.
+/2 width=3 by lsubr_inv_abst2_aux/ qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma lsubr_fwd_pair2: ∀I2,L1,K2,V2. L1 ⫃ K2.ⓑ{I2}V2 →
+                       ∃∃I1,K1,V1. K1 ⫃ K2 & L1 = K1.ⓑ{I1}V1.
+* #L1 #K2 #V2 #H
+[ elim (lsubr_inv_abbr2 … H) | elim (lsubr_inv_abst2 … H) * ] -H
+/2 width=5 by ex2_3_intro/
 qed-.