X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Fssta2%2Fssta_lift.etc;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fetc%2Fssta2%2Fssta_lift.etc;h=5398364e0c5c94f80a7374662a80e9f9ba76f891;hb=ff7754f834f937bfe2384c7703cf63f552885395;hp=0000000000000000000000000000000000000000;hpb=4720368dcf18593959c6d21484f62fb5b61f3d26;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/ssta2/ssta_lift.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/ssta2/ssta_lift.etc
new file mode 100644
index 000000000..5398364e0
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/ssta2/ssta_lift.etc
@@ -0,0 +1,119 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/relocation/ldrop_ldrop.ma".
+include "basic_2/static/ssta.ma".
+
+(* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
+
+(* Properties on relocation *************************************************)
+
+lemma ssta_lift: ∀h,g,G,L1,T1,U1,l. ⦃G, L1⦄ ⊢ T1 •[h, g] ⦃l, U1⦄ →
+                 ∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
+                 ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃G, L2⦄ ⊢ T2 •[h, g] ⦃l, U2⦄.
+#h #g #G #L1 #T1 #U1 #l #H elim H -G -L1 -T1 -U1 -l
+[ #G #L1 #k #l #Hkl #L2 #d #e #HL21 #X1 #H1 #X2 #H2
+  >(lift_inv_sort1 … H1) -X1
+  >(lift_inv_sort1 … H2) -X2 /2 width=1/
+| #G #L1 #K1 #V1 #W1 #W #i #l #HLK1 #_ #HW1 #IHVW1 #L2 #d #e #HL21 #X #H #U2 #HWU2
+  elim (lift_inv_lref1 … H) * #Hid #H destruct
+  [ elim (lift_trans_ge … HW1 … HWU2 ?) -W // #W2 #HW12 #HWU2
+    elim (ldrop_trans_le … HL21 … HLK1 ?) -L1 /2 width=2/ #X #HLK2 #H
+    elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #K2 #V2 #HK21 #HV12 #H destruct
+    /3 width=8/
+  | lapply (lift_trans_be … HW1 … HWU2 ? ?) -W // /2 width=1/ #HW1U2
+    lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 // -Hid /3 width=8/
+  ]
+| #G #L1 #K1 #W1 #V1 #W #i #l #HLK1 #_ #HW1 #IHWV1 #L2 #d #e #HL21 #X #H #U2 #HWU2
+  elim (lift_inv_lref1 … H) * #Hid #H destruct
+  [ elim (lift_trans_ge … HW1 … HWU2 ?) -W // <minus_plus #W #HW1 #HWU2
+    elim (ldrop_trans_le … HL21 … HLK1 ?) -L1 /2 width=2/ #X #HLK2 #H
+    elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ -Hid #K2 #W2 #HK21 #HW12 #H destruct
+    lapply (lift_mono … HW1 … HW12) -HW1 #H destruct
+    elim (lift_total V1 (d-i-1) e) /3 width=8/
+  | lapply (lift_trans_be … HW1 … HWU2 ? ?) -W // /2 width=1/ #HW1U2
+    lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 // -Hid /3 width=8/
+  ]
+| #a #I #G #L1 #V1 #T1 #U1 #l #_ #IHTU1 #L2 #d #e #HL21 #X1 #H1 #X2 #H2
+  elim (lift_inv_bind1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H destruct
+  elim (lift_inv_bind1 … H2) -H2 #X #U2 #H1 #HU12 #H2 destruct
+  lapply (lift_mono … H1 … HV12) -H1 #H destruct /4 width=5/
+| #G #L1 #V1 #T1 #U1 #l #_ #IHTU1 #L2 #d #e #HL21 #X1 #H1 #X2 #H2
+  elim (lift_inv_flat1 … H1) -H1 #V2 #T2 #HV12 #HT12 #H destruct
+  elim (lift_inv_flat1 … H2) -H2 #X #U2 #H1 #HU12 #H2 destruct
+  lapply (lift_mono … H1 … HV12) -H1 #H destruct /4 width=5/
+| #G #L1 #W1 #T1 #U1 #l #_ #IHTU1 #L2 #d #e #HL21 #X #H #U2 #HU12
+  elim (lift_inv_flat1 … H) -H #W2 #T2 #HW12 #HT12 #H destruct /3 width=5/
+]
+qed.
+
+lemma ssta_inv_lift1: ∀h,g,G,L2,T2,U2,l. ⦃G, L2⦄ ⊢ T2 •[h, g] ⦃l, U2⦄ →
+                      ∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
+                      ∃∃U1. ⦃G, L1⦄ ⊢ T1 •[h, g] ⦃l, U1⦄ & ⇧[d, e] U1 ≡ U2.
+#h #g #G #L2 #T2 #U2 #l #H elim H -G -L2 -T2 -U2 -l
+[ #G #L2 #k #l #Hkl #L1 #d #e #_ #X #H
+  >(lift_inv_sort2 … H) -X /3 width=3/
+| #G #L2 #K2 #V2 #W2 #W #i #l #HLK2 #HVW2 #HW2 #IHVW2 #L1 #d #e #HL21 #X #H
+  elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HVW2 | -IHVW2 ]
+  [ elim (ldrop_conf_lt … HL21 … HLK2 ?) -L2 // #K1 #V1 #HLK1 #HK21 #HV12
+    elim (IHVW2 … HK21 … HV12) -K2 -V2 #W1 #HVW1 #HW12
+    elim (lift_trans_le … HW12 … HW2 ?) -W2 // >minus_plus <plus_minus_m_m // -Hid /3 width=6/
+  | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 // #HL1K2
+    elim (le_inv_plus_l … Hid) -Hid #Hdie #ei
+    elim (lift_split … HW2 d (i-e+1) ? ? ?) -HW2 // [3: /2 width=1/ ]
+    [ #W0 #HW20 <le_plus_minus_comm // >minus_minus_m_m /2 width=1/ /3 width=6/
+    | <le_plus_minus_comm //
+    ]
+  ]
+| #G #L2 #K2 #W2 #V2 #W #i #l #HLK2 #HWV2 #HW2 #IHWV2 #L1 #d #e #HL21 #X #H
+  elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HWV2 | -IHWV2 ]
+  [ elim (ldrop_conf_lt … HL21 … HLK2 ?) -L2 // #K1 #W1 #HLK1 #HK21 #HW12
+    elim (IHWV2 … HK21 … HW12) -K2 #V1 #HWV1 #_
+    elim (lift_trans_le … HW12 … HW2 ?) -W2 // >minus_plus <plus_minus_m_m // -Hid /3 width=6/
+  | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 // #HL1K2
+    elim (le_inv_plus_l … Hid) -Hid #Hdie #ei
+    elim (lift_split … HW2 d (i-e+1) ? ? ?) -HW2 // [3: /2 width=1/ ]
+    [ #W0 #HW20 <le_plus_minus_comm // >minus_minus_m_m /2 width=1/ /3 width=6/
+    | <le_plus_minus_comm //
+    ]
+  ]
+| #a #I #G #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #d #e #HL21 #X #H
+  elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
+  elim (IHTU2 (L1.ⓑ{I}V1) … HT12) -IHTU2 -HT12 /2 width=1/ -HL21 /3 width=5/
+| #G #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #d #e #HL21 #X #H
+  elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct
+  elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=5/
+| #G #L2 #W2 #T2 #U2 #l #_ #IHTU2 #L1 #d #e #HL21 #X #H
+  elim (lift_inv_flat2 … H) -H #W1 #T1 #HW12 #HT12 #H destruct
+  elim (IHTU2 … HL21 … HT12) -L2 -HT12 /3 width=3/
+]
+qed-.
+
+(* Advanced forvard lemmas **************************************************)
+
+lemma ssta_fwd_correct: ∀h,g,G,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U⦄ →
+                        ∃T0. ⦃G, L⦄ ⊢ U •[h, g] ⦃l-1, T0⦄.
+#h #g #G #L #T #U #l #H elim H -G -L -T -U -l
+[ /4 width=2/
+| #G #L #K #V #W #W0 #i #l #HLK #_ #HW0 * #V0 #HWV0
+  lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
+  elim (lift_total V0 0 (i+1)) /3 width=10/
+| #G #L #K #W #V #V0 #i #l #HLK #HWV #HWV0 #_
+  lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
+  elim (lift_total V 0 (i+1)) /3 width=10/
+| #a #I #G #L #V #T #U #l #_ * /3 width=2/
+| #G #L #V #T #U #l #_ * #T0 #HUT0 /3 width=2/
+| #G #L #W #T #U #l #_ * /2 width=2/
+]
+qed-.