matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_ssta.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/equivalence/cpcs_cpcs.ma".
  16 include "basic_2/dynamic/lsubsv_ldrop.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  19
  20 (* Properties on stratified native type assignment **************************)
  21
  22 lemma lsubsv_ssta_trans: ∀h,g,L2,T,U2,l. ⦃h, L2⦄ ⊢ T •[g,l] U2 →
  23                          ∀L1. h ⊢ L1 ⊩:⊑[g] L2 →
  24                          ∃∃U1. L1 ⊢ U2 ⬌* U1 & ⦃h, L1⦄ ⊢ T •[g,l] U1.
  25 #h #g #L2 #T #U2 #l #H elim H -L2 -T -U2 -l
  26 [ #L2 #k #l #Hkl #L1 #_ /3 width=3/
  27 | #L2 #K2 #V2 #W2 #U2 #i #l #HLK2 #_ #HWU2 #IHVW2 #L1 #HL12
  28   elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  29   elim (lsubsv_inv_pair2 … H) -H *
  30   [ #K1 #HK12 #H destruct
  31     elim (IHVW2 … HK12) -K2 #W1 #HW21 #H
  32     elim (lift_total W1 0 (i+1)) #U1 #HWU1
  33     lapply (ldrop_fwd_ldrop2 … HLK1) /3 width=9/
  34   | #K1 #V1 #W1 #l0 #_ #_ #_ #_ #_ #_ #H destruct
  35   ]
  36 | #L2 #K2 #W2 #V2 #U2 #i #l #HLK2 #_ #HWU2 #IHWV2 #L1 #HL12
  37   elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  38   elim (lsubsv_inv_pair2 … H) -H *
  39   [ #K1 #HK12 #H destruct
  40     elim (IHWV2 … HK12) -K2 #V1 #_ #H -V2 /3 width=6/
  41   | #K1 #W1 #V1 #l0 #HV1 #HVW1 #HW21 #HW2 #HK12 #H #_ destruct
  42     elim (IHWV2 … HK12) -K2 #V #_ #H
  43     elim (lift_total W1 0 (i+1)) #U1 #HWU1
  44     lapply (ldrop_fwd_ldrop2 … HLK1) #HLK
  45     @(ex2_intro … U1)
  46     [ @(cpcs_lift … HLK … HWU2 … HWU1 HW21)
  47     | @(ssta_ldef … HLK1 … HWU1)
  48   (*
  49     /3 width=9/
  50   *)