X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flsubd.ma;h=29da4dad7b28b298a51023fbd11875eb6bbadf04;hb=a961a1237063702ed9c32a9a4b7994671cb40818;hp=5e2332c7c8c641bd12fc5a8cab0c16f038c474ca;hpb=fdb2c62b58006b82c015ba70b494d50c7860e28f;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma
index 5e2332c7c..29da4dad7 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lrsubeqd_5.ma".
-include "basic_2/substitution/lsubr.ma".
+include "basic_2/static/lsubr.ma".
 include "basic_2/static/da.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR DEGREE ASSIGNMENT ***********************)
@@ -22,7 +22,7 @@ inductive lsubd (h) (g) (G): relation lenv ≝
 | lsubd_atom: lsubd h g G (⋆) (⋆)
 | lsubd_pair: ∀I,L1,L2,V. lsubd h g G L1 L2 →
               lsubd h g G (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsubd_abbr: ∀L1,L2,W,V,l. ⦃G, L1⦄ ⊢ V ▪[h, g] l+1 → ⦃G, L2⦄ ⊢ W ▪[h, g] l →
+| lsubd_beta: ∀L1,L2,W,V,d. ⦃G, L1⦄ ⊢ V ▪[h, g] d+1 → ⦃G, L2⦄ ⊢ W ▪[h, g] d →
               lsubd h g G L1 L2 → lsubd h g G (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
@@ -30,122 +30,122 @@ interpretation
   "local environment refinement (degree assignment)"
   'LRSubEqD h g G L1 L2 = (lsubd h g G L1 L2).
 
-(* Basic_forward lemmas *****************************************************)
+(* Basic forward lemmas *****************************************************)
 
-lemma lsubd_fwd_lsubr: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 → L1 ⊑ L2.
-#h #g #G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
+lemma lsubd_fwd_lsubr: ∀h,g,G,L1,L2. G ⊢ L1 ⫃▪[h, g] L2 → L1 ⫃ L2.
+#h #g #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubr_pair, lsubr_beta/
 qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubd_inv_atom1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 → L1 = ⋆ → L2 = ⋆.
+fact lsubd_inv_atom1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⫃▪[h, g] L2 → L1 = ⋆ → L2 = ⋆.
 #h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #W #V #l #_ #_ #_ #H destruct
+| #L1 #L2 #W #V #d #_ #_ #_ #H destruct
 ]
 qed-.
 
-lemma lsubd_inv_atom1: ∀h,g,G,L2. G ⊢ ⋆ ▪⊑[h, g] L2 → L2 = ⋆.
+lemma lsubd_inv_atom1: ∀h,g,G,L2. G ⊢ ⋆ ⫃▪[h, g] L2 → L2 = ⋆.
 /2 width=6 by lsubd_inv_atom1_aux/ qed-.
 
-fact lsubd_inv_pair1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 →
+fact lsubd_inv_pair1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⫃▪[h, g] L2 →
                           ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (∃∃K2. G ⊢ K1 ▪⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
-                          ∃∃K2,W,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                      G ⊢ K1 ▪⊑[h, g] K2 &
+                          (∃∃K2. G ⊢ K1 ⫃▪[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                          ∃∃K2,W,V,d. ⦃G, K1⦄ ⊢ V ▪[h, g] d+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] d &
+                                      G ⊢ K1 ⫃▪[h, g] K2 &
                                       I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 #h #g #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 #l #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 #d #HV #HW #HL12 #J #K1 #X #H destruct /3 width=9 by ex6_4_intro, or_intror/
 ]
 qed-.
 
-lemma lsubd_inv_pair1: ∀h,g,I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ▪⊑[h, g] L2 →
-                       (∃∃K2. G ⊢ K1 ▪⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
-                       ∃∃K2,W,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                   G ⊢ K1 ▪⊑[h, g] K2 &
+lemma lsubd_inv_pair1: ∀h,g,I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ⫃▪[h, g] L2 →
+                       (∃∃K2. G ⊢ K1 ⫃▪[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                       ∃∃K2,W,V,d. ⦃G, K1⦄ ⊢ V ▪[h, g] d+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] d &
+                                   G ⊢ K1 ⫃▪[h, g] K2 &
                                    I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsubd_inv_pair1_aux/ qed-.
 
-fact lsubd_inv_atom2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 → L2 = ⋆ → L1 = ⋆.
+fact lsubd_inv_atom2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⫃▪[h, g] L2 → L2 = ⋆ → L1 = ⋆.
 #h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
-| #L1 #L2 #W #V #l #_ #_ #_ #H destruct
+| #L1 #L2 #W #V #d #_ #_ #_ #H destruct
 ]
 qed-.
 
-lemma lsubd_inv_atom2: ∀h,g,G,L1. G ⊢ L1 ▪⊑[h, g] ⋆ → L1 = ⋆.
+lemma lsubd_inv_atom2: ∀h,g,G,L1. G ⊢ L1 ⫃▪[h, g] ⋆ → L1 = ⋆.
 /2 width=6 by lsubd_inv_atom2_aux/ qed-.
 
-fact lsubd_inv_pair2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 →
+fact lsubd_inv_pair2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ⫃▪[h, g] L2 →
                           ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                          (∃∃K1. G ⊢ K1 ▪⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
-                          ∃∃K1,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                    G ⊢ K1 ▪⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+                          (∃∃K1. G ⊢ K1 ⫃▪[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                          ∃∃K1,V,d. ⦃G, K1⦄ ⊢ V ▪[h, g] d+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] d &
+                                    G ⊢ K1 ⫃▪[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 #h #g #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 #l #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 #d #HV #HW #HL12 #J #K2 #U #H destruct /3 width=7 by ex5_3_intro, or_intror/
 ]
 qed-.
 
-lemma lsubd_inv_pair2: ∀h,g,I,G,L1,K2,W. G ⊢ L1 ▪⊑[h, g] K2.ⓑ{I}W →
-                       (∃∃K1. G ⊢ K1 ▪⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
-                       ∃∃K1,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                 G ⊢ K1 ▪⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+lemma lsubd_inv_pair2: ∀h,g,I,G,L1,K2,W. G ⊢ L1 ⫃▪[h, g] K2.ⓑ{I}W →
+                       (∃∃K1. G ⊢ K1 ⫃▪[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                       ∃∃K1,V,d. ⦃G, K1⦄ ⊢ V ▪[h, g] d+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] d &
+                                 G ⊢ K1 ⫃▪[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 /2 width=3 by lsubd_inv_pair2_aux/ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsubd_refl: ∀h,g,G,L. G ⊢ L ▪⊑[h, g] L.
-#h #g #G #L elim L -L // /2 width=1/
+lemma lsubd_refl: ∀h,g,G,L. G ⊢ L ⫃▪[h, g] L.
+#h #g #G #L elim L -L /2 width=1 by lsubd_pair/
 qed.
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsubd_ldrop_O1_conf: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 →
-                           ∀K1,e. ⇩[0, e] L1 ≡ K1 →
-                           ∃∃K2. G ⊢ K1 ▪⊑[h, g] K2 & ⇩[0, e] L2 ≡ K2.
+lemma lsubd_drop_O1_conf: ∀h,g,G,L1,L2. G ⊢ L1 ⫃▪[h, g] L2 →
+                          ∀K1,s,m. ⬇[s, 0, m] L1 ≡ K1 →
+                          ∃∃K2. G ⊢ K1 ⫃▪[h, g] K2 & ⬇[s, 0, m] L2 ≡ K2.
 #h #g #G #L1 #L2 #H elim H -L1 -L2
-[ /2 width=3/
-| #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #V #_ #IHL12 #K1 #s #m #H
+  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK1
   [ destruct
-    elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK1) -L1 /3 width=3/
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsubd_pair, drop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by drop_drop_lt, ex2_intro/
   ]
-| #L1 #L2 #W #V #l #HV #HW #_ #IHL12 #K1 #e #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+| #L1 #L2 #W #V #d #HV #HW #_ #IHL12 #K1 #s #m #H
+  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK1
   [ destruct
-    elim (IHL12 L1 0) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK1) -L1 /3 width=3/
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsubd_beta, drop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by drop_drop_lt, ex2_intro/
   ]
 ]
 qed-.
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsubd_ldrop_O1_trans: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 →
-                            ∀K2,e. ⇩[0, e] L2 ≡ K2 →
-                            ∃∃K1. G ⊢ K1 ▪⊑[h, g] K2 & ⇩[0, e] L1 ≡ K1.
+lemma lsubd_drop_O1_trans: ∀h,g,G,L1,L2. G ⊢ L1 ⫃▪[h, g] L2 →
+                           ∀K2,s,m. ⬇[s, 0, m] L2 ≡ K2 →
+                           ∃∃K1. G ⊢ K1 ⫃▪[h, g] K2 & ⬇[s, 0, m] L1 ≡ K1.
 #h #g #G #L1 #L2 #H elim H -L1 -L2
-[ /2 width=3/
-| #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #V #_ #IHL12 #K2 #s #m #H
+  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK2
   [ destruct
-    elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK2) -L2 /3 width=3/
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsubd_pair, drop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
   ]
-| #L1 #L2 #W #V #l #HV #HW #_ #IHL12 #K2 #e #H
-  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+| #L1 #L2 #W #V #d #HV #HW #_ #IHL12 #K2 #s #m #H
+  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK2
   [ destruct
-    elim (IHL12 L2 0) -IHL12 // #X #HL12 #H
-    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3/
-  | elim (IHL12 … HLK2) -L2 /3 width=3/
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsubd_beta, drop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
   ]
 ]
 qed-.