X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flsubr.ma;h=382458d9eb2fb22e7a5a67d00320473569804a1b;hp=e96683a80e96fc536957699695a2065bc013b7e4;hb=222044da28742b24584549ba86b1805a87def070;hpb=944b1f7b762774a6f8d99a2c2846f865b6788712

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
index e96683a80..382458d9e 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
@@ -12,96 +12,165 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lrsubeq_2.ma".
-include "basic_2/relocation/ldrop.ma".
+include "basic_2/notation/relations/lrsubeqc_2.ma".
+include "basic_2/syntax/lenv.ma".
 
-(* RESTRICTED LOCAL ENVIRONMENT REFINEMENT **********************************)
+(* RESTRICTED REFINEMENT FOR LOCAL ENVIRONMENTS *****************************)
 
+(* Basic_2A1: just tpr_cpr and tprs_cprs require the extended lsubr_atom *)
+(* Basic_2A1: includes: lsubr_pair *)
 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: lsubr (⋆) (⋆)
+| lsubr_bind: ∀I,L1,L2. lsubr L1 L2 → lsubr (L1.ⓘ{I}) (L2.ⓘ{I})
+| lsubr_beta: ∀L1,L2,V,W. lsubr L1 L2 → lsubr (L1.ⓓⓝW.V) (L2.ⓛW)
+| lsubr_unit: ∀I1,I2,L1,L2,V. lsubr L1 L2 → lsubr (L1.ⓑ{I1}V) (L2.ⓤ{I2})
 .
 
 interpretation
-  "local environment refinement (restricted)"
-  'LRSubEq L1 L2 = (lsubr L1 L2).
+  "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/
+lemma lsubr_refl: ∀L. L ⫃ L.
+#L elim L -L /2 width=1 by lsubr_atom, lsubr_bind/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubr_inv_atom1_aux: ∀L1,L2. L1 ⊑ L2 → L1 = ⋆ → L2 = ⋆.
+fact lsubr_inv_atom1_aux: ∀L1,L2. L1 ⫃ L2 → L1 = ⋆ → L2 = ⋆.
 #L1 #L2 * -L1 -L2 //
-[ #I #L1 #L2 #V #_ #H destruct
+[ #I #L1 #L2 #_ #H destruct
 | #L1 #L2 #V #W #_ #H destruct
+| #I1 #I2 #L1 #L2 #V #_ #H destruct  
 ]
 qed-.
 
-lemma lsubr_inv_atom1: ∀L2. ⋆ ⊑ L2 → L2 = ⋆.
+lemma lsubr_inv_atom1: ∀L2. ⋆ ⫃ L2 → L2 = ⋆.
 /2 width=3 by lsubr_inv_atom1_aux/ qed-.
 
-fact lsubr_inv_abst1_aux: ∀L1,L2. L1 ⊑ L2 → ∀K1,W. L1 = K1.ⓛW →
-                          L2 = ⋆ ∨ ∃∃K2. K1 ⊑ K2 & L2 = K2.ⓛW.
+fact lsubr_inv_bind1_aux: ∀L1,L2. L1 ⫃ L2 → ∀I,K1. L1 = K1.ⓘ{I} →
+                          ∨∨ ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓘ{I}
+                           | ∃∃K2,V,W. K1 ⫃ K2 & L2 = K2.ⓛW &
+                                       I = BPair Abbr (ⓝW.V)
+                           | ∃∃J1,J2,K2,V. K1 ⫃ K2 & L2 = K2.ⓤ{J2} &
+                                           I = BPair J1 V.
 #L1 #L2 * -L1 -L2
-[ #L #K1 #W #H destruct /2 width=1 by or_introl/
-| #I #L1 #L2 #V #HL12 #K1 #W #H destruct /3 width=3 by ex2_intro, or_intror/
-| #L1 #L2 #V1 #V2 #_ #K1 #W #H destruct
+[ #J #K1 #H destruct
+| #I #L1 #L2 #HL12 #J #K1 #H destruct /3 width=3 by or3_intro0, ex2_intro/
+| #L1 #L2 #V #W #HL12 #J #K1 #H destruct /3 width=6 by or3_intro1, ex3_3_intro/
+| #I1 #I2 #L1 #L2 #V #HL12 #J #K1 #H destruct /3 width=4 by or3_intro2, ex3_4_intro/
 ]
 qed-.
 
-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-.
+(* Basic_2A1: uses: lsubr_inv_pair1 *)
+lemma lsubr_inv_bind1: ∀I,K1,L2. K1.ⓘ{I} ⫃ L2 →
+                       ∨∨ ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓘ{I}
+                        | ∃∃K2,V,W. K1 ⫃ K2 & L2 = K2.ⓛW &
+                                    I = BPair Abbr (ⓝW.V)
+                        | ∃∃J1,J2,K2,V. K1 ⫃ K2 & L2 = K2.ⓤ{J2} &
+                                        I = BPair J1 V.
+/2 width=3 by lsubr_inv_bind1_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_atom2_aux: ∀L1,L2. L1 ⫃ L2 → L2 = ⋆ → L1 = ⋆.
+#L1 #L2 * -L1 -L2 //
+[ #I #L1 #L2 #_ #H destruct
+| #L1 #L2 #V #W #_ #H destruct
+| #I1 #I2 #L1 #L2 #V #_ #H destruct
+]
+qed-.
+
+lemma lsubr_inv_atom2: ∀L1. L1 ⫃ ⋆ → L1 = ⋆.
+/2 width=3 by lsubr_inv_atom2_aux/ qed-.
+
+fact lsubr_inv_bind2_aux: ∀L1,L2. L1 ⫃ L2 → ∀I,K2. L2 = K2.ⓘ{I} →
+                          ∨∨ ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓘ{I}
+                           | ∃∃K1,W,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V & I = BPair Abst W
+                           | ∃∃J1,J2,K1,V. K1 ⫃ K2 & L1 = K1.ⓑ{J1}V & I = BUnit J2.
 #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
+[ #J #K2 #H destruct
+| #I #L1 #L2 #HL12 #J #K2 #H destruct /3 width=3 by ex2_intro, or3_intro0/
+| #L1 #L2 #V1 #V2 #HL12 #J #K2 #H destruct /3 width=6 by ex3_3_intro, or3_intro1/
+| #I1 #I2 #L1 #L2 #V #HL12 #J #K2 #H destruct /3 width=5 by ex3_4_intro, or3_intro2/
 ]
 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_bind2: ∀I,L1,K2. L1 ⫃ K2.ⓘ{I} →
+                       ∨∨ ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓘ{I}
+                        | ∃∃K1,W,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V & I = BPair Abst W
+                        | ∃∃J1,J2,K1,V. K1 ⫃ K2 & L1 = K1.ⓑ{J1}V & I = BUnit J2.
+/2 width=3 by lsubr_inv_bind2_aux/ qed-.
 
-(* Basic forward lemmas *****************************************************)
+(* Advanced inversion lemmas ************************************************)
+
+lemma lsubr_inv_abst1: ∀K1,L2,W. K1.ⓛW ⫃ L2 →
+                       ∨∨ ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓛW
+                        | ∃∃I2,K2. K1 ⫃ K2 & L2 = K2.ⓤ{I2}.
+#K1 #L2 #W #H elim (lsubr_inv_bind1 … H) -H *
+/3 width=4 by ex2_2_intro, ex2_intro, or_introl, or_intror/ 
+#K2 #V2 #W2 #_ #_ #H destruct
+qed-.
+
+lemma lsubr_inv_unit1: ∀I,K1,L2. K1.ⓤ{I} ⫃ L2 →
+                       ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓤ{I}.
+#I #K1 #L2 #H elim (lsubr_inv_bind1 … H) -H *
+[ #K2 #HK12 #H destruct /2 width=3 by ex2_intro/
+| #K2 #V #W #_ #_ #H destruct
+| #I1 #I2 #K2 #V #_ #_ #H destruct
+]
+qed-.
 
-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_pair2: ∀I,L1,K2,W. L1 ⫃ K2.ⓑ{I}W →
+                       ∨∨ ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓑ{I}W
+                        | ∃∃K1,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V & I = Abst.
+#I #L1 #K2 #W #H elim (lsubr_inv_bind2 … H) -H *
+[ /3 width=3 by ex2_intro, or_introl/
+| #K2 #X #V #HK12 #H1 #H2 destruct /3 width=4 by ex3_2_intro, or_intror/
+| #I1 #I1 #K2 #V #_ #_ #H destruct   
+]
+qed-.
+
+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 *
+[ /2 width=3 by ex2_intro/
+| #K1 #X #_ #_ #H destruct
+]
+qed-.
+
+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 *
+/3 width=4 by ex2_2_intro, ex2_intro, or_introl, or_intror/
 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/
-  ]
+lemma lsubr_inv_unit2: ∀I,L1,K2. L1 ⫃ K2.ⓤ{I} →
+                       ∨∨ ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓤ{I}
+                        | ∃∃J,K1,V. K1 ⫃ K2 & L1 = K1.ⓑ{J}V.
+#I #L1 #K2 #H elim (lsubr_inv_bind2 … H) -H *
+[ /3 width=3 by ex2_intro, or_introl/
+| #K1 #W #V #_ #_ #H destruct
+| #I1 #I2 #K1 #V #HK12 #H1 #H2 destruct /3 width=5 by ex2_3_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
+(* Basic forward lemmas *****************************************************)
+
+lemma lsubr_fwd_bind1: ∀I1,K1,L2. K1.ⓘ{I1} ⫃ L2 →
+                       ∃∃I2,K2. K1 ⫃ K2 & L2 = K2.ⓘ{I2}.
+#I1 #K1 #L2 #H elim (lsubr_inv_bind1 … H) -H *
+[ #K2 #HK12 #H destruct /3 width=4 by ex2_2_intro/
+| #K2 #W1 #V1 #HK12 #H1 #H2 destruct /3 width=4 by ex2_2_intro/
+| #I1 #I2 #K2 #V1 #HK12 #H1 #H2 destruct /3 width=4 by ex2_2_intro/
+]
+qed-.
+
+lemma lsubr_fwd_bind2: ∀I2,L1,K2. L1 ⫃ K2.ⓘ{I2} →
+                       ∃∃I1,K1. K1 ⫃ K2 & L1 = K1.ⓘ{I1}.
+#I2 #L1 #K2 #H elim (lsubr_inv_bind2 … H) -H *
+[ #K1 #HK12 #H destruct /3 width=4 by ex2_2_intro/
+| #K1 #W1 #V1 #HK12 #H1 #H2 destruct /3 width=4 by ex2_2_intro/
+| #I1 #I2 #K1 #V1 #HK12 #H1 #H2 destruct /3 width=4 by ex2_2_intro/
+]
 qed-.