matita/matita/contribs/lambda_delta/basic_2/static/ssta_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_lift.ma".
  16 include "basic_2/static/ssta.ma".
  17
  18 (* STRATIFIED STATIC TYPE ASSIGNMENT ON TERMS *******************************)
  19
  20 (* Properties on atomic arity assignment for terms **************************)
  21
  22 lemma ssta_aaa: ∀h,g,L,T,A. L ⊢ T ⁝ A → ∀U,l. ⦃h, L⦄ ⊢ T •[g, l] U → L ⊢ U ⁝ A.
  23 #h #g #L #T #A #H elim H -L -T -A
  24 [ #L #k #U #l #H
  25   elim (ssta_inv_sort1 … H) -H #_ #H destruct //
  26 | #I #L #K #V #B #i #HLK #HV #IHV #U #l #H
  27   elim (ssta_inv_lref1 … H) -H * #K0 #V0 #W0 [2: #l0 ] #HLK0 #HVW0 #HU [ #H ]
  28   lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H0 destruct
  29   lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
  30   @(aaa_lift … HLK … HU) -HU -L // -HV /2 width=2/
  31 | #a #L #V #T #B #A #HV #_ #_ #IHT #X #l #H
  32   elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
  33 | #a #L #V #T #B #A #HV #_ #_ #IHT #X #l #H
  34   elim (ssta_inv_bind1 … H) -H #U #HTU #H destruct /3 width=2/
  35 | #L #V #T #B #A #HV #_ #_ #IHT #X #l #H
  36   elim (ssta_inv_appl1 … H) -H #U #HTU #H destruct /3 width=3/
  37 | #L #V #T #A #_ #_ #IHV #IHT #X #l #H
  38   lapply (ssta_inv_cast1 … H) -H /2 width=2/
  39 ]
  40 qed.
  41