- lambdadelta: third recursive part of preservation finally proved!

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma
index 04f7dcb4c98ac2de251ccc0ee84dabb8f475c86e..f3238fbd9cc57fae42cc247c2c740a493714f102 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/computation/dxprs_dxprs.ma".
 include "basic_2/dynamic/snv_cpcs.ma".
 
 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
@@ -19,23 +20,24 @@ include "basic_2/dynamic/snv_cpcs.ma".
 (* Properties on context-free parallel reduction for local environments *****)
 
 fact snv_ltpr_tpr_aux: ∀h,g,L0,T0.
+                       (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
                        ∀L1,T1. L0 = L1 → T0 = T1 → IH_snv_ltpr_tpr h g L1 T1.
-#h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 * * [||||*]
-[ #k #HL0 #HT0 #H1 #L2 #_ #X #H2 destruct -IH3 -IH2 -IH1 -L1
+#h #g #L0 #T0 #IH4 #IH3 #IH2 #IH1 #L1 * * [||||*]
+[ #k #HL0 #HT0 #H1 #L2 #_ #X #H2 destruct -IH4 -IH3 -IH2 -IH1 -L1
   >(tpr_inv_atom1 … H2) -X //
-| #i #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH3 -IH2
+| #i #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH4 -IH3 -IH2
   elim (snv_inv_lref … H1) -H1 #I #K1 #V1 #HLK1 #HV1
   >(tpr_inv_atom1 … H2) -X
   elim (ltpr_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
   elim (ltpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
   lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) -HLK1 #HLK1
   lapply (IH1 … HK12 … HV12) -IH1 -HV12 -HK12 // -HV1 [ /2 width=1/ ] -HLK1 /2 width=5/
-| #p #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH3 -IH2 -IH1
+| #p #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH4 -IH3 -IH2 -IH1
   elim (snv_inv_gref … H1)
-| #a #I #V1 #T1 #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH3 -IH2
+| #a #I #V1 #T1 #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH4 -IH3 -IH2
   elim (snv_inv_bind … H1) -H1 #HV1 #HT1
   elim (tpr_inv_bind1 … H2) -H2 *
   [ #V2 #T0 #T2 #HV12 #HT10 #HT02 #H destruct
@@ -50,15 +52,29 @@ fact snv_ltpr_tpr_aux: ∀h,g,L0,T0.
 | #V1 #T1 #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct
   elim (snv_inv_appl … H1) -H1 #a #W10 #W1 #U1 #l #HV1 #HT1 #HVW1 #HW10 #HTU1
   elim (tpr_inv_appl1 … H2) -H2 *
-  [ #V2 #T2 #HV12 #HT12 #H destruct
+  [ #V2 #T2 #HV12 #HT12 #H destruct -IH4
     lapply (IH1 … HV1 … HL12 … HV12) [ /2 width=1/ ] #HV2
     lapply (IH1 … HT1 … HL12 … HT12) [ /2 width=1/ ] #HT2
     elim (IH3 … HVW1 … HL12 … HV12) -HVW1 -HV12 // -HV1 [2: /2 width=1/ ] #W2 #HVW2 #HW12
-    lapply (cpcs_cprs_conf … HW10 … HW12) -W10 #HW12
-    elim (dxprs_cprs_aux … IH2 IH1 IH3 … T2 … HTU1) // [2: /3 width=1/ |3: /2 width=1/ ] -IH2 -IH1 -IH3 -HT1 -HT12 -HTU1 #U2 #HTU2 #HU12
-    @(snv_appl … HV2 HT2 HVW2)
-(*
-    lapply (IH1 … HT1 … HTU1) -IH1 // #H
-    elim (snv_inv_bind … H) -H #HW1 #HU1
-    elim (IH2 … HVW1 … HL12 … HV12 HV1) -IH2 -HVW1 -HV12 -HV1 // #W2 #HVW2 #HW12
-*)
+    elim (dxprs_ltpr_cprs_aux … IH2 IH1 IH3 … HTU1 … HL12 T2) // [2: /3 width=1/ |3: /2 width=1/ ] -IH2 -IH1 -IH3 -HT1 -HT12 -HTU1 #X #HTU2 #H
+    elim (cprs_inv_abst1 Abst W1 … H) -H #W20 #U2 #HW120 #_ #H destruct
+    lapply (ltpr_cprs_conf … HL12 … HW10) -L1 #HW10
+    lapply (cpcs_cprs_strap1 … HW10 … HW120) -W1 #HW120
+    lapply (cpcs_canc_sn … HW12 HW120) -W10 #HW20
+    elim (cpcs_inv_cprs … HW20) -HW20 #W0 #HW20 #HW200
+    lapply (dxprs_cprs_trans … (ⓛ{a}W0.U2) HTU2 ?) [ /2 width=1/ ] -HW200 /2 width=8/
+  | #b #V2 #W20 #T20 #T2 #HV12 #HT202 #H1 #H2 destruct
+    elim (snv_inv_bind … HT1) -HT1 #HW20 #HT20
+    elim (dxprs_inv_abst1 … HTU1) -HTU1 #W30 #T30 #HW230 #_ #H destruct -T30
+    lapply (cprs_div … HW230 … HW10) -W30 #HW210
+    lapply (ltpr_cpcs_conf … HL12 … HW210) -HW210 #HW210
+    lapply (IH1 … HL12 … HV12) // [ /2 width=1/ ] #HV2
+    lapply (IH1 … HW20 … HL12 W20 ?) // [ /2 width=1/ ] -HW20 #HW20
+    lapply (IH1 … HT20 … (L2.ⓛW20) … HT202) [1,2: /2 width=1/ ] -IH1 -HT20 -HT202 #HT2
+    elim (IH3 … HVW1 … HL12 … HV12) // [2: /2 width=1/ ] -HV1 -HVW1 -HV12 #W200 #HVW200 #H
+    lapply (cpcs_trans … HW210 … H) -W10 #HW200
+    lapply (IH4 … HT2 (L2.ⓓV2) ?) -HT2
+    [ (* /2 width=4/ *)
+    |
+    | /2 width=1/
+    ]