matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_snv.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/lsubsv_ldrop.ma".
  17 include "basic_2/dynamic/lsubsv_dxprs.ma".
  18 include "basic_2/dynamic/lsubsv_cpcs.ma".
  19
  20 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  21
  22 (* Properties concerning stratified native validity *************************)
  23
  24 fact snv_lsubsv_aux: ∀h,g,L0,T0.
  25                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
  26                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
  27                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
  28                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
  29                      ∀L1,T1. L0 = L1 → T0 = T1 → IH_snv_lsubsv h g L1 T1.
  30 #h #g #L0 #T0 #IH4 #IH3 #IH2 #IH1 #L2 * * [||||*] //
  31 [ #i #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
  32   elim (snv_inv_lref … H) -H #I2 #K2 #W2 #HLK2 #HW2
  33   elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -HL12 #X #H #HLK1
  34   lapply (ldrop_pair2_fwd_fw … HLK2 (#i)) -HLK2 #HLK2
  35   elim (lsubsv_inv_pair2 … H) -H * #K1
  36   [ #HK12 #H destruct /4 width=8 by snv_lref, fw_ygt/ (**) (* auto too slow without trace *)
  37   | #W1 #V1 #V2 #l #HV1 #_ #_ #_ #_ #_ #H #_ destruct /2 width=5/
  38   ]
  39 | #p #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2 -IH1
  40   elim (snv_inv_gref … H)
  41 | #a #I #V #T #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
  42   elim (snv_inv_bind … H) -H /4 width=4/
  43 | #V #T #HL0 #HT0 #H #L1 #HL12 destruct
  44   elim (snv_inv_appl … H) -H #a #W #W0 #U #l #HV #HT #HVW #HW0 #HTU
  45   lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
  46   elim (lsubsv_ssta_trans … HVW … HL12) -HVW #W1 #HVW1 #HW1
  47   lapply (cpcs_cprs_strap1 … HW1 … HW0) -W #HW10
  48   elim (dxprs_lsubsv_aux … IH4 IH3 IH2 IH1 … HL12 … HTU) -IH4 -IH3 -IH2 -HTU // /2 width=1/ #X #HTU #H
  49   elim (cprs_inv_abst1 Abst W0 … H) -H #W #U2 #HW0 #HU2 #H destruct
  50   lapply (cpcs_cprs_strap1 … HW10 … HW0) -W0 #H
  51   elim (cpcs_inv_cprs … H) -H #W0 #HW10 #HW0
  52   lapply (dxprs_cprs_trans … (ⓛ{a}W0.U2) HTU ?) [ /2 width=1/ ] -HTU -HW0
  53   /4 width=8 by snv_appl, fw_ygt/ (**) (* auto too slow without trace *)
  54 | #W #T #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
  55   elim (snv_inv_cast … H) -H #U #l #HW #HT #HTU #HUW
  56   lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
  57   elim (lsubsv_ssta_trans … HTU … HL12) -HTU #U0 #HTU0 #HU0
  58   lapply (cpcs_trans … HU0 … HUW) -U /4 width=4 by snv_cast, fw_ygt/ (**) (* auto too slow without trace *)
  59 ]
  60 qed-.