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/dynamic/lsubsv_ldrop.ma".
  16 include "basic_2/dynamic/lsubsv_cpcs.ma".
  17 (*
  18 include "basic_2/dynamic/lsubsv_ssta.ma".
  19 *)
  20 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  21
  22 (* Properties concerning stratified native validity *************************)
  23 (*
  24 axiom lsubsv_xprs_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
  25                          ∀T1,T2. ⦃h, L2⦄ ⊢ T1 •➡*[g] T2 → ⦃h, L1⦄ ⊢ T1 •➡*[g] T2.
  26
  27 /3 width=3 by lsubsv_fwd_lsubss, lsubss_xprs_trans/ qed-.
  28 *)
  29 lemma lsubsv_snv_trans: ∀h,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
  30                         ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
  31 #h #g #L2 #T #H elim H -L2 -T //
  32 [ #I2 #L2 #K2 #W2 #i #HLK2 #_ #IHW2 #L1 #HL12
  33   elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  34   elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -IHW2 ]
  35   [ #HK12 #H destruct /3 width=5/
  36   | #W1 #V1 #l #HV1 #_ #_ #_ #_ #H #_ destruct /2 width=5/
  37   ]
  38 | #a #I #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 /4 width=1/
  39 | #a #L2 #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
  40   lapply (IHV … HL12) -IHV #HV
  41   lapply (IHT … HL12) -IHT #HT
  42   lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
  43 (*
  44   lapply (lsubsv_ssta_trans … HVW … HL12) -HVW #HVW
  45   lapply (lsubsv_xprs_trans … HL12 … HTU) -HL12 -HTU /2 width=8/
  46 *)
  47 | #L2 #W #T #U #l #_ #_ #HTU #HUW #IHW #IHT #L1 #HL12
  48   lapply (IHW … HL12) -IHW #HW
  49   lapply (IHT … HL12) -IHT #HT
  50   lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
  51 (*
  52   lapply (lsubsv_ssta_trans … HTU … HL12) -HTU #HTU
  53 -HL12 -HWU /2 width=4/
  54 ]
  55 qed-.
  56 *)