matita/matita/contribs/lambdadelta/basic_2A/static/lsuba_aaa.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_2A/static/aaa_aaa.ma".
  16 include "basic_2A/static/lsuba.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
  19
  20 (* Properties concerning atomic arity assignment ****************************)
  21
  22 lemma lsuba_aaa_conf: ∀G,L1,V,A. ⦃G, L1⦄ ⊢ V ⁝ A →
  23                       ∀L2. G ⊢ L1 ⫃⁝ L2 → ⦃G, L2⦄ ⊢ V ⁝ A.
  24 #G #L1 #V #A #H elim H -G -L1 -V -A
  25 [ //
  26 | #I #G #L1 #K1 #V #A #i #HLK1 #HV #IHV #L2 #HL12
  27   elim (lsuba_drop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
  28   elim (lsuba_inv_pair1 … H) -H * #K2
  29   [ #HK12 #H destruct /3 width=5 by aaa_lref/
  30   | #W0 #V0 #A0 #HV0 #HW0 #_ #H1 #H2 #H3 destruct
  31     lapply (aaa_mono … HV0 … HV) #H destruct -V0 /2 width=5 by aaa_lref/
  32   ]
  33 | /4 width=2 by lsuba_pair, aaa_abbr/
  34 | /4 width=1 by lsuba_pair, aaa_abst/
  35 | /3 width=3 by aaa_appl/
  36 | /3 width=1 by aaa_cast/
  37 ]
  38 qed-.
  39
  40 lemma lsuba_aaa_trans: ∀G,L2,V,A. ⦃G, L2⦄ ⊢ V ⁝ A →
  41                        ∀L1. G ⊢ L1 ⫃⁝ L2 → ⦃G, L1⦄ ⊢ V ⁝ A.
  42 #G #L2 #V #A #H elim H -G -L2 -V -A
  43 [ //
  44 | #I #G #L2 #K2 #V #A #i #HLK2 #H1V #IHV #L1 #HL12
  45   elim (lsuba_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  46   elim (lsuba_inv_pair2 … H) -H * #K1
  47   [ #HK12 #H destruct /3 width=5 by aaa_lref/
  48   | #V0 #A0 #HV0 #H2V #_ #H1 #H2 destruct
  49     lapply (aaa_mono … H2V … H1V) #H destruct -K2 /2 width=5 by aaa_lref/
  50   ]
  51 | /4 width=2 by lsuba_pair, aaa_abbr/
  52 | /4 width=1 by lsuba_pair, aaa_abst/
  53 | /3 width=3 by aaa_appl/
  54 | /3 width=1 by aaa_cast/
  55 ]
  56 qed-.