matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_ltpr.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/computation/dxprs_dxprs.ma".
  16 include "basic_2/dynamic/snv_cpcs.ma".
  17
  18 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
  19
  20 (* Properties on context-free parallel reduction for local environments *****)
  21
  22 fact snv_ltpr_tpr_aux: ∀h,g,L0,T0.
  23                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
  24                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
  25                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
  26                        ∀L1,T1. L0 = L1 → T0 = T1 → IH_snv_ltpr_tpr h g L1 T1.
  27 #h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 * * [||||*]
  28 [ #k #HL0 #HT0 #H1 #L2 #_ #X #H2 destruct -IH3 -IH2 -IH1 -L1
  29   >(tpr_inv_atom1 … H2) -X //
  30 | #i #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH3 -IH2
  31   elim (snv_inv_lref … H1) -H1 #I #K1 #V1 #HLK1 #HV1
  32   >(tpr_inv_atom1 … H2) -X
  33   elim (ltpr_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
  34   elim (ltpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
  35   lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) -HLK1 #HLK1
  36   lapply (IH1 … HK12 … HV12) -IH1 -HV12 -HK12 // -HV1 [ /2 width=1/ ] -HLK1 /2 width=5/
  37 | #p #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH3 -IH2 -IH1
  38   elim (snv_inv_gref … H1)
  39 | #a #I #V1 #T1 #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct -IH3 -IH2
  40   elim (snv_inv_bind … H1) -H1 #HV1 #HT1
  41   elim (tpr_inv_bind1 … H2) -H2 *
  42   [ #V2 #T0 #T2 #HV12 #HT10 #HT02 #H destruct
  43     lapply (tps_lsubs_trans … HT02 (L2.ⓑ{I}V2) ?) -HT02 /2 width=1/ #HT02
  44     lapply (IH1 … HL12 … HV12) // [ /2 width=1/ ] #HV2
  45     lapply (snv_ltpr_cpr_aux … HT1  (L2.ⓑ{I}V2) … T2 ?) -HT1
  46     [ /3 width=5 by cpr_intro, tps_tpss/ | /2 width=1/ | /3 width=1/ ] -IH1 -T0 /2 width=1/
  47   | #T2 #HT12 #HXT2 #H1 #H2 destruct
  48     lapply (IH1 … HT1 (L2.ⓓV1) … HT12) -IH1 -HT1 -HT12 [1,2: /2 width=1/ ] -HL12 #HT2
  49     lapply (snv_inv_lift … HT2 L2 … HXT2) -T2 // /2 width=1/
  50   ]
  51 | #V1 #T1 #HL0 #HT0 #H1 #L2 #HL12 #X #H2 destruct
  52   elim (snv_inv_appl … H1) -H1 #a #W10 #W1 #U1 #l #HV1 #HT1 #HVW1 #HW10 #HTU1
  53   elim (tpr_inv_appl1 … H2) -H2 *
  54   [ #V2 #T2 #HV12 #HT12 #H destruct
  55     lapply (IH1 … HV1 … HL12 … HV12) [ /2 width=1/ ] #HV2
  56     lapply (IH1 … HT1 … HL12 … HT12) [ /2 width=1/ ] #HT2
  57     elim (IH3 … HVW1 … HL12 … HV12) -HVW1 -HV12 // -HV1 [2: /2 width=1/ ] #W2 #HVW2 #HW12
  58     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
  59     elim (cprs_inv_abst1 Abst W1 … H) -H #W20 #U2 #HW120 #_ #H destruct
  60     lapply (ltpr_cprs_conf … HL12 … HW10) -L1 #HW10
  61     lapply (cpcs_cprs_strap1 … HW10 … HW120) -W1 #HW120
  62     lapply (cpcs_canc_sn … HW12 HW120) -W10 #HW20
  63     elim (cpcs_inv_cprs … HW20) -HW20 #W0 #HW20 #HW200
  64     lapply (dxprs_cprs_trans … (ⓛ{a}W0.U2) HTU2 ?) [ /2 width=1/ ] -HW200 /2 width=8/