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

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  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/static/ssta_ssta.ma".
  16 include "basic_2/equivalence/cpcs_cpcs.ma".
  17 include "basic_2/dynamic/lsubsv_ldrop.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
  20
  21 (* Properties on stratified static type assignment **************************)
  22
  23 lemma lsubsv_ssta_trans: ∀h,g,L2,T,U2,l. ⦃h, L2⦄ ⊢ T •[h, g] ⦃l, U2⦄ →
  24                          ∀L1. h ⊢ L1 ¡⊑[h, g] L2 →
  25                          ∃∃U1. ⦃h, L1⦄ ⊢ T •[h, g] ⦃l, U1⦄ & L1 ⊢ U1 ⬌* U2.
  26 #h #g #L2 #T #U #l #H elim H -L2 -T -U -l
  27 [ /3 width=3/
  28 | #L2 #K2 #X #Y #U #i #l #HLK2 #_ #HYU #IHXY #L1 #HL12
  29   elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  30   elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -HYU -IHXY -HLK1 ]
  31   [ #HK12 #H destruct
  32     elim (IHXY … HK12) -K2 #T #HXT #HTY
  33     lapply (ldrop_fwd_ldrop2 … HLK1) #H
  34     elim (lift_total T 0 (i+1)) /3 width=11/
  35   | #V #W1 #V2 #l0 #_ #_ #_ #_ #_ #H destruct
  36   ]
  37 | #L2 #K2 #Y #X #U #i #l #HLK2 #HYX #HYU #IHYX #L1 #HL12
  38   elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  39   elim (lsubsv_inv_pair2 … H) -H * #K1 [ -HYX | -IHYX ]
  40   [ #HK12 #H destruct
  41     elim (IHYX … HK12) -K2 /3 width=6/
  42   | #V #W1 #V2 #l0 #HYV #_ #HV #HY #_ #_ #H destruct
  43     elim (snv_inv_cast … HYV) -HYV #W #l1 #_ #_ #HVW #HWY
  44     elim (ssta_mono … HVW … HV) -HV #Hl10 #_
  45     elim (ssta_mono … HYX … HY) -HYX -HY #H #_ destruct
  46     lapply (ldrop_fwd_ldrop2 … HLK1) #H
  47     elim (lift_total W 0 (i+1))
  48     /4 width=11 by cpcs_lift, ex2_intro, ssta_ldef, ssta_cast/
  49   ]
  50 | #a #I #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
  51   elim (IHTU2 (L1.ⓑ{I}V2) …) [2: /2 width=1/ ] -L2 /3 width=3/
  52 | #L2 #V2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
  53   elim (IHTU2 … HL12) -L2 /3 width=5/
  54 | #L2 #W2 #T2 #U2 #l #_ #IHTU2 #L1 #HL12
  55   elim (IHTU2 … HL12) -L2 /3 width=3/
  56 ]
  57 qed-.