reorganization of the "static" component:

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
index 49441a887da6be0dc9793192991855772bc72661..a353d95dfb10169a7bbcff032ad8912e3abb5c8a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lrsubeqa_3.ma".
-include "basic_2/relocation/lsubr.ma".
+include "basic_2/static/lsubr.ma".
 include "basic_2/static/aaa.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
@@ -31,7 +31,7 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsuba_inv_atom1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → L1 = ⋆ → L2 = ⋆.
+fact lsuba_inv_atom1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → L1 = ⋆ → L2 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -39,27 +39,27 @@ fact lsuba_inv_atom1_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → L1 = ⋆ → L2 = 
 ]
 qed-.
 
-lemma lsuba_inv_atom1: â\88\80G,L2. G â\8a¢ â\8b\86 â\81\9dâ\8a\91 L2 → L2 = ⋆.
+lemma lsuba_inv_atom1: â\88\80G,L2. G â\8a¢ â\8b\86 â\81\9dâ«\83 L2 → L2 = ⋆.
 /2 width=4 by lsuba_inv_atom1_aux/ qed-.
 
-fact lsuba_inv_pair1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L2 = K2.ⓑ{I}X) ∨
+fact lsuba_inv_pair1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
+                          (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & L2 = K2.ⓑ{I}X) ∨
                           ∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                      G â\8a¢ K1 â\81\9dâ\8a\91 K2 & I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
+                                      G â\8a¢ K1 â\81\9dâ«\83 K2 & I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 #G #L1 #L2 * -L1 -L2
 [ #J #K1 #X #H destruct
-| #I #L1 #L2 #V #HL12 #J #K1 #X #H destruct /3 width=3/
-| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K1 #X #H destruct /3 width=9/
+| #I #L1 #L2 #V #HL12 #J #K1 #X #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K1 #X #H destruct /3 width=9 by or_intror, ex6_4_intro/
 ]
 qed-.
 
-lemma lsuba_inv_pair1: â\88\80I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\81\9dâ\8a\91 L2 →
-                       (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L2 = K2.ⓑ{I}X) ∨
-                       â\88\83â\88\83K2,W,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ\8a\91 K2 &
+lemma lsuba_inv_pair1: â\88\80I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\81\9dâ«\83 L2 →
+                       (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & L2 = K2.ⓑ{I}X) ∨
+                       â\88\83â\88\83K2,W,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ«\83 K2 &
                                    I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsuba_inv_pair1_aux/ qed-.
 
-fact lsuba_inv_atom2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → L2 = ⋆ → L1 = ⋆.
+fact lsuba_inv_atom2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → L2 = ⋆ → L1 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -67,34 +67,78 @@ fact lsuba_inv_atom2_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → L2 = ⋆ → L1 = 
 ]
 qed-.
 
-lemma lsubc_inv_atom2: â\88\80G,L1. G â\8a¢ L1 â\81\9dâ\8a\91 ⋆ → L1 = ⋆.
+lemma lsubc_inv_atom2: â\88\80G,L1. G â\8a¢ L1 â\81\9dâ«\83 ⋆ → L1 = ⋆.
 /2 width=4 by lsuba_inv_atom2_aux/ qed-.
 
-fact lsuba_inv_pair2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                          (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L1 = K1.ⓑ{I}W) ∨
+fact lsuba_inv_pair2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
+                          (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & L1 = K1.ⓑ{I}W) ∨
                           ∃∃K1,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                    G â\8a¢ K1 â\81\9dâ\8a\91 K2 & I = Abst & L1 = K1.ⓓⓝW.V.
+                                    G â\8a¢ K1 â\81\9dâ«\83 K2 & I = Abst & L1 = K1.ⓓⓝW.V.
 #G #L1 #L2 * -L1 -L2
 [ #J #K2 #U #H destruct
-| #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3/
-| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K2 #U #H destruct /3 width=7/
+| #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K2 #U #H destruct /3 width=7 by or_intror, ex5_3_intro/
 ]
 qed-.
 
-lemma lsuba_inv_pair2: â\88\80I,G,L1,K2,W. G â\8a¢ L1 â\81\9dâ\8a\91 K2.ⓑ{I}W →
-                       (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ\8a\91 K2 & L1 = K1.ⓑ{I}W) ∨
-                       â\88\83â\88\83K1,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ\8a\91 K2 &
+lemma lsuba_inv_pair2: â\88\80I,G,L1,K2,W. G â\8a¢ L1 â\81\9dâ«\83 K2.ⓑ{I}W →
+                       (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & L1 = K1.ⓑ{I}W) ∨
+                       â\88\83â\88\83K1,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ«\83 K2 &
                                  I = Abst & L1 = K1.ⓓⓝW.V.
 /2 width=3 by lsuba_inv_pair2_aux/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lsuba_fwd_lsubr: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ\8a\91 L2 â\86\92 L1 â\8a\91 L2.
-#G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
+lemma lsuba_fwd_lsubr: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 â\86\92 L1 â«\83 L2.
+#G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubr_bind, lsubr_abst/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsuba_refl: â\88\80G,L. G â\8a¢ L â\81\9dâ\8a\91 L.
-#G #L elim L -L // /2 width=1/
+lemma lsuba_refl: â\88\80G,L. G â\8a¢ L â\81\9dâ«\83 L.
+#G #L elim L -L /2 width=1 by lsuba_atom, lsuba_pair/
 qed.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsuba_ldrop_O1_conf: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+                           ∃∃K2. G ⊢ K1 ⁝⫃ K2 & ⇩[s, 0, e] L2 ≡ K2.
+#G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K1 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+]
+qed-.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsuba_ldrop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
+                            ∃∃K1. G ⊢ K1 ⁝⫃ K2 & ⇩[s, 0, e] L1 ≡ K1.
+#G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K2 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+]
+qed-.