reorganization of the "static" component:

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / lsubsv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
index fa872435e03fd970575e32a1289d35153f4220ac..7d1faa892fe5763d3c9709757af400832f83da3f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
@@ -34,7 +34,7 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubsv_inv_atom1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â\8a\91[h, g] L2 → L1 = ⋆ → L2 = ⋆.
+fact lsubsv_inv_atom1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â«\83[h, g] L2 → L1 = ⋆ → L2 = ⋆.
 #h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -42,16 +42,16 @@ fact lsubsv_inv_atom1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 → L1 = ⋆
 ]
 qed-.
 
-lemma lsubsv_inv_atom1: â\88\80h,g,G,L2. G â\8a¢ â\8b\86 ¡â\8a\91[h, g] L2 → L2 = ⋆.
+lemma lsubsv_inv_atom1: â\88\80h,g,G,L2. G â\8a¢ â\8b\86 ¡â«\83[h, g] L2 → L2 = ⋆.
 /2 width=6 by lsubsv_inv_atom1_aux/ qed-.
 
-fact lsubsv_inv_pair1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â\8a\91[h, g] L2 →
+fact lsubsv_inv_pair1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â«\83[h, g] L2 →
                            ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                           (â\88\83â\88\83K2. G â\8a¢ K1 ¡â\8a\91[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                           (â\88\83â\88\83K2. G â\8a¢ K1 ¡â«\83[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
                            ∃∃K2,W,V,l. ⦃G, K1⦄ ⊢ W ¡[h, g] & ⦃G, K1⦄ ⊢ V ¡[h, g] &
                                        scast h g l G K1 V W & ⦃G, K2⦄ ⊢ W ¡[h, g] &
                                        ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                       G â\8a¢ K1 ¡â\8a\91[h, g] K2 &
+                                       G â\8a¢ K1 ¡â«\83[h, g] K2 &
                                        I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 #h #g #G #L1 #L2 * -L1 -L2
 [ #J #K1 #X #H destruct
@@ -60,16 +60,16 @@ fact lsubsv_inv_pair1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 →
 ]
 qed-.
 
-lemma lsubsv_inv_pair1: â\88\80h,g,I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X ¡â\8a\91[h, g] L2 →
-                        (â\88\83â\88\83K2. G â\8a¢ K1 ¡â\8a\91[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+lemma lsubsv_inv_pair1: â\88\80h,g,I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X ¡â«\83[h, g] L2 →
+                        (â\88\83â\88\83K2. G â\8a¢ K1 ¡â«\83[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
                         ∃∃K2,W,V,l. ⦃G, K1⦄ ⊢ W ¡[h, g] & ⦃G, K1⦄ ⊢ V ¡[h, g] &
                                     scast h g l G K1 V W & ⦃G, K2⦄ ⊢ W ¡[h, g] &
                                     ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                    G â\8a¢ K1 ¡â\8a\91[h, g] K2 &
+                                    G â\8a¢ K1 ¡â«\83[h, g] K2 &
                                     I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsubsv_inv_pair1_aux/ qed-.
 
-fact lsubsv_inv_atom2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â\8a\91[h, g] L2 → L2 = ⋆ → L1 = ⋆.
+fact lsubsv_inv_atom2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â«\83[h, g] L2 → L2 = ⋆ → L1 = ⋆.
 #h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -77,16 +77,16 @@ fact lsubsv_inv_atom2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 → L2 = ⋆
 ]
 qed-.
 
-lemma lsubsv_inv_atom2: â\88\80h,g,G,L1. G â\8a¢ L1 ¡â\8a\91[h, g] ⋆ → L1 = ⋆.
+lemma lsubsv_inv_atom2: â\88\80h,g,G,L1. G â\8a¢ L1 ¡â«\83[h, g] ⋆ → L1 = ⋆.
 /2 width=6 by lsubsv_inv_atom2_aux/ qed-.
 
-fact lsubsv_inv_pair2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â\8a\91[h, g] L2 →
+fact lsubsv_inv_pair2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â«\83[h, g] L2 →
                            ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                           (â\88\83â\88\83K1. G â\8a¢ K1 ¡â\8a\91[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                           (â\88\83â\88\83K1. G â\8a¢ K1 ¡â«\83[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
                            ∃∃K1,V,l. ⦃G, K1⦄ ⊢ W ¡[h, g] & ⦃G, K1⦄ ⊢ V ¡[h, g] &
                                      scast h g l G K1 V W & ⦃G, K2⦄ ⊢ W ¡[h, g] &
                                      ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                     G â\8a¢ K1 ¡â\8a\91[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+                                     G â\8a¢ K1 ¡â«\83[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/
@@ -94,27 +94,73 @@ fact lsubsv_inv_pair2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ¡⊑[h, g] L2 →
 ]
 qed-.
 
-lemma lsubsv_inv_pair2: â\88\80h,g,I,G,L1,K2,W. G â\8a¢ L1 ¡â\8a\91[h, g] K2.ⓑ{I}W →
-                        (â\88\83â\88\83K1. G â\8a¢ K1 ¡â\8a\91[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+lemma lsubsv_inv_pair2: â\88\80h,g,I,G,L1,K2,W. G â\8a¢ L1 ¡â«\83[h, g] K2.ⓑ{I}W →
+                        (â\88\83â\88\83K1. G â\8a¢ K1 ¡â«\83[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
                         ∃∃K1,V,l. ⦃G, K1⦄ ⊢ W ¡[h, g] & ⦃G, K1⦄ ⊢ V ¡[h, g] &
                                   scast h g l G K1 V W & ⦃G, K2⦄ ⊢ W ¡[h, g] &
                                   ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                  G â\8a¢ K1 ¡â\8a\91[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+                                  G â\8a¢ K1 ¡â«\83[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 /2 width=3 by lsubsv_inv_pair2_aux/ qed-.
 
 (* Basic_forward lemmas *****************************************************)
 
-lemma lsubsv_fwd_lsubr: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â\8a\91[h, g] L2 â\86\92 L1 â\8a\91 L2.
+lemma lsubsv_fwd_lsubr: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â«\83[h, g] L2 â\86\92 L1 â«\83 L2.
 #h #g #G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsubsv_refl: â\88\80h,g,G,L. G â\8a¢ L ¡â\8a\91[h, g] L.
+lemma lsubsv_refl: â\88\80h,g,G,L. G â\8a¢ L ¡â«\83[h, g] L.
 #h #g #G #L elim L -L // /2 width=1/
 qed.
 
-lemma lsubsv_cprs_trans: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â\8a\91[h, g] L2 →
+lemma lsubsv_cprs_trans: â\88\80h,g,G,L1,L2. G â\8a¢ L1 ¡â«\83[h, g] L2 →
                          ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ➡* T2 → ⦃G, L1⦄ ⊢ T1 ➡* T2.
 /3 width=6 by lsubsv_fwd_lsubr, lsubr_cprs_trans/
 qed-.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsubsv_ldrop_O1_conf: ∀h,g,G,L1,L2. G ⊢ L1 ¡⫃[h, g] L2 →
+                            ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+                            ∃∃K2. G ⊢ K1 ¡⫃[h, g] K2 & ⇩[s, 0, e] L2 ≡ K2.
+#h #g #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 lsubsv_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #l #H1W #HV #HVW #H2W #H1l #H2l #_ #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=4 by lsubsv_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 lsubsv_ldrop_O1_trans: ∀h,g,G,L1,L2. G ⊢ L1 ¡⫃[h, g] L2 →
+                             ∀K2,s, e. ⇩[s, 0, e] L2 ≡ K2 →
+                             ∃∃K1. G ⊢ K1 ¡⫃[h, g] K2 & ⇩[s, 0, e] L1 ≡ K1.
+#h #g #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 lsubsv_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #l #H1W #HV #HVW #H2W #H1l #H2l #_ #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=4 by lsubsv_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+]
+qed-.