X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2A%2Fdynamic%2Fsnv_lpr.ma;fp=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2A%2Fdynamic%2Fsnv_lpr.ma;h=78f7e59f8bb96f2290ff447e8d5cc96170562282;hb=d2545ffd201b1aa49887313791386add78fa8603;hp=0000000000000000000000000000000000000000;hpb=57ae1762497a5f3ea75740e2908e04adb8642cc2;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/dynamic/snv_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2A/dynamic/snv_lpr.ma
new file mode 100644
index 000000000..78f7e59f8
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2A/dynamic/snv_lpr.ma
@@ -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_2A/dynamic/snv_lift.ma".
+include "basic_2A/dynamic/snv_aaa.ma".
+include "basic_2A/dynamic/snv_scpes.ma".
+include "basic_2A/dynamic/lsubsv_snv.ma".
+
+(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
+
+(* Properties on context-free parallel reduction for local environments *****)
+
+fact snv_cpr_lpr_aux: ∀h,g,G0,L0,T0.
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_lstas h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_lstas_cpr_lpr h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_da_cpr_lpr h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) →
+                      ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_snv_cpr_lpr h g G1 L1 T1.
+#h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ]
+[ #k #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #_ destruct -IH4 -IH3 -IH2 -IH1 -H1
+  >(cpr_inv_sort1 … H2) -X //
+| #i #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2
+  elim (snv_inv_lref … H1) -H1 #I #K1 #V1 #HLK1 #HV1
+  elim (lpr_drop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
+  elim (lpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
+  lapply (fqup_lref … G1 … HLK1) #HKL
+  elim (cpr_inv_lref1 … H2) -H2
+  [ #H destruct -HLK1 /4 width=10 by fqup_fpbg, snv_lref/
+  | * #K0 #V0 #W0 #H #HVW0 #W0 -HV12
+    lapply (drop_mono … H … HLK1) -HLK1 -H #H destruct
+    lapply (drop_fwd_drop2 … HLK2) -HLK2 /4 width=8 by fqup_fpbg, snv_lift/
+  ]
+| #p #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2 -IH1
+  elim (snv_inv_gref … H1)
+| #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2
+  elim (snv_inv_bind … H1) -H1 #HV1 #HT1
+  elim (cpr_inv_bind1 … H2) -H2 *
+  [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=8 by fqup_fpbg, snv_bind, lpr_pair/
+  | #T2 #HT12 #HXT2 #H1 #H2 destruct -HV1
+    /4 width=10 by fqup_fpbg, snv_inv_lift, lpr_pair, drop_drop/
+  ]
+| #V1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct
+  elim (snv_inv_appl … H1) -H1 #a #W1 #U1 #d0 #HV1 #HT1 #HVW1 #HTU1
+  elim (cpr_inv_appl1 … H2) -H2 *
+  [ #V2 #T2 #HV12 #HT12 #H destruct -IH4
+    lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
+    lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ #HT2
+    elim (scpds_cpr_lpr_aux … IH2 IH3 … HVW1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HVW1 -HV12 #XV #HVW2 #HXV
+    elim (scpds_cpr_lpr_aux … IH2 IH3 … HTU1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ -HTU1 -HT12 #X #HTU2 #H
+    elim (cprs_inv_abst1 … H) -H #XW #U2 #HXW #_ #H destruct -IH1 -IH3 -IH2 -L1
+    elim (cprs_conf … HXV … HXW) -W1 #W2 #HXV #HXW
+    lapply (scpds_cprs_trans … HVW2 … HXV) -XV
+    lapply (scpds_cprs_trans … (ⓛ{a}W2.U2) … HTU2 ?)
+    /2 width=7 by snv_appl, cprs_bind/
+  | #b #V2 #W10 #W20 #T10 #T20 #HV12 #HW120 #HT120 #H1 #H2 destruct
+    elim (snv_inv_bind … HT1) -HT1 #HW10 #HT10
+    elim (scpds_inv_abst1 … HTU1) -HTU1 #W30 #T30 #HW130 #_ #H destruct -T30 -d0
+    elim (snv_fwd_da … HV1) #d #HV1d
+    elim (snv_fwd_da … HW10) #d0 #HW10d
+    lapply (cprs_scpds_div … HW130 … HW10d … 1 HVW1) -W30 #HVW10
+    elim (da_scpes_aux … IH4 IH1 IH2 … HW10d … HV1d … HVW10) /2 width=1 by fqup_fpbg/
+    #_ #Hd <minus_n_O #H destruct >(plus_minus_m_m d 1) in HV1d; // -Hd #HV1d
+    lapply (scpes_cpr_lpr_aux … IH2 IH3 … HVW10 … HW120 … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HVW10 #HVW20
+    lapply (IH2 … HV1d … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HV1d #HV2d
+    lapply (IH2 … HW10d … HW120 … HL12) /2 width=1 by fqup_fpbg/ -HW10d #HW20d
+    lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
+    lapply (IH1 … HW120 … HL12) /2 width=1 by fqup_fpbg/ -HW10 #HW20
+    lapply (IH1 … HT10 … HT120 … (L2.ⓛW20) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -HT10 #HT20
+    @snv_bind /2 width=1 by snv_cast_scpes/
+    @(lsubsv_snv_trans … HT20) -HT20
+    @(lsubsv_beta … (d-1)) //
+    @shnv_cast [1,2: // ] #d0 #Hd0
+    lapply (scpes_le_aux … IH4 IH1 IH2 IH3 … HW20d … HV2d … d0 … HVW20) -IH4 -IH3 -IH2 -IH1 -HW20d -HV2d -HVW20
+    /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs, le_S_S/
+  | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -IH4
+    elim (snv_inv_bind … HT1) -HT1 #HW0 #HT0
+    elim (scpds_inv_abbr_abst … HTU1) -HTU1 #X #HTU0 #HX #H destruct
+    elim (lift_inv_bind1 … HX) -HX #W3 #U3 #HW13 #_ #H destruct
+    elim (scpds_cpr_lpr_aux … IH2 IH3 … HVW1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ -HVW1 #XV #HXV0 #HXVW1
+    elim (scpds_cpr_lpr_aux … IH2 IH3 … HTU0 … HT02 (L2.ⓓW2)) /2 width=1 by fqup_fpbg, lpr_pair/ -HTU0 #X #HXT2 #H
+    elim (cprs_inv_abst1 … H) -H #W #U2 #HW3 #_ #H destruct -U3
+    lapply (IH1 … HW02 … HL12) /2 width=1 by fqup_fpbg/ #HW2
+    lapply (IH1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ #HV0
+    lapply (IH1 … HT02 (L2.ⓓW2) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -L1 #HT2
+    lapply (snv_lift … HV0 (L2.ⓓW2) (Ⓕ) … HV02) /2 width=1 by drop_drop/ -HV0 #HV2
+    elim (lift_total XV 0 1) #XW #HXVW
+    lapply (scpds_lift … HXV0 (L2.ⓓW2) (Ⓕ) … HV02 … HXVW) /2 width=1 by drop_drop/ -V0 #HXWV2
+    lapply (cprs_lift … HXVW1 (L2.ⓓW2) (Ⓕ) … HW13 … HXVW) /2 width=1 by drop_drop/ -W1 -XV #HXW3
+    elim (cprs_conf … HXW3 … HW3) -W3 #W3 #HXW3 #HW3
+    lapply (scpds_cprs_trans … HXWV2 … HXW3) -XW
+    lapply (scpds_cprs_trans … (ⓛ{a}W3.U2) … HXT2 ?) /2 width=1 by cprs_bind/ -W
+    /3 width=6 by snv_appl, snv_bind/
+  ]
+| #W1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4
+  elim (snv_inv_cast … H1) -H1 #U1 #HW1 #HT1 #HWU1 #HTU1
+  elim (cpr_inv_cast1 … H2) -H2
+  [ * #W2 #T2 #HW12 #HT12 #H destruct
+    elim (snv_fwd_da … HW1) #d #HW1d
+    lapply (scpds_div … HWU1 … HTU1) -U1 -d #HWT1
+    lapply (scpes_cpr_lpr_aux … IH2 IH3 … HWT1 … HW12 … HT12 … HL12) /2 width=1 by fqup_fpbg/
+    lapply (IH1 … HW12 … HL12) /2 width=1 by fqup_fpbg/
+    lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ -L1
+    /2 width=1 by snv_cast_scpes/
+  | #H -IH3 -IH2 -HW1 -U1
+    lapply (IH1 … H … HL12) /2 width=1 by fqup_fpbg/
+  ]
+]
+qed-.