matita/matita/contribs/lambdadelta/basic_2/etc/snta/lsubsn_snta.etc

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/snta_snta.ma".
  16 include "basic_2/dynamic/lsubsn_ldrop.ma".
  17 include "basic_2/dynamic/lsubsn_cpcs.ma".
  18
  19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE TYPE ASSIGNMENT *******)
  20
  21 (* Properties concerning stratified native type assignment ******************)
  22
  23 (* Note: the corresponding confluence property does not hold *)
  24 lemma lsubsn_snta_trans: ∀h,L2,T,U,l. ⦃h, L2⦄ ⊢ T :[l] U →
  25                          ∀L1. h ⊢ L1 :⊑[] L2 → ⦃h, L1⦄ ⊢ T :[l] U.
  26 #h #L2 #T #U #l #H elim H -L2 -T -U -l
  27 [ //
  28 | #L2 #K2 #V2 #W2 #U2 #i #l #HLK2 #_ #WU2 #IHVW2 #L1 #HL12
  29   elim (lsubsn_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  30   elim (lsubsn_inv_pair2 … H) -H * #K1
  31   [ #HK12 #H destruct /3 width=6/
  32   | #V1 #l0 #_ #_ #_ #_ #H destruct
  33   ]
  34 | #L2 #K2 #W2 #V2 #U2 #i #l #HLK2 #HWV2 #HWU2 #IHWV2 #L1 #HL12
  35   elim (lsubsn_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  36   elim (lsubsn_inv_pair2 … H) -H * #K1 [ -HWV2 | -IHWV2 ]
  37   [ #HK12 #H destruct /3 width=6/
  38   | #V1 #l0 #H1 #H2 #_ #H #_ destruct
  39     elim (snta_fwd_correct … H2) -H2 #V #H
  40     elim (snta_mono … HWV2 … H) -HWV2 -H /2 width=6/
  41   ]
  42 | /4 width=3/
  43 | /3 width=2/
  44 | /3 width=2/
  45 | /3 width=1/
  46 | #L2 #T #U1 #U2 #V2 #l #_ #HU12 #_ #IHTU1 #IHUV2 #L1 #HL12
  47   lapply (cpcs_lsubsn_trans … HL12 … HU12) -HU12 /3 width=3/
  48 ]
  49 qed.