matita/matita/contribs/lambdadelta/basic_2/static/lsuba_aaa.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/static/aaa_aaa.ma".
  16 include "basic_2/static/lsuba_ldrop.ma".
  17
  18 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
  19
  20 (* Properties concerning atomic arity assignment ****************************)
  21
  22 lemma lsuba_aaa_conf: ∀L1,V,A. L1 ⊢ V ⁝ A → ∀L2. L1 ⁝⊑ L2 → L2 ⊢ V ⁝ A.
  23 #L1 #V #A #H elim H -L1 -V -A
  24 [ //
  25 | #I #L1 #K1 #V #A #i #HLK1 #HV #IHV #L2 #HL12
  26   elim (lsuba_ldrop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
  27   elim (lsuba_inv_pair1 … H) -H * #K2
  28   [ #HK12 #H destruct /3 width=5/
  29   | #W0 #V0 #A0 #HV0 #HW0 #_ #H1 #H2 #H3 destruct
  30     lapply (aaa_mono … HV0 … HV) #H destruct -V0 /2 width=5/
  31   ]
  32 | /4 width=2/
  33 | /4 width=1/
  34 | /3 width=3/
  35 | /3 width=1/
  36 ]
  37 qed-.
  38
  39 lemma lsuba_aaa_trans: ∀L2,V,A. L2 ⊢ V ⁝ A → ∀L1. L1 ⁝⊑ L2 → L1 ⊢ V ⁝ A.
  40 #L2 #V #A #H elim H -L2 -V -A
  41 [ //
  42 | #I #L2 #K2 #V #A #i #HLK2 #H1V #IHV #L1 #HL12
  43   elim (lsuba_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
  44   elim (lsuba_inv_pair2 … H) -H * #K1
  45   [ #HK12 #H destruct /3 width=5/
  46   | #V0 #A0 #HV0 #H2V #_ #H1 #H2 destruct
  47     lapply (aaa_mono … H2V … H1V) #H destruct -K2 /2 width=5/
  48   ]
  49 | /4 width=2/
  50 | /4 width=1/
  51 | /3 width=3/
  52 | /3 width=1/
  53 ]
  54 qed-.