matita/matita/contribs/lambdadelta/basic_2A/static/da_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_lift.ma".
  16 include "basic_2A/static/da.ma".
  17
  18 (* DEGREE ASSIGNMENT FOR TERMS **********************************************)
  19
  20 (* Properties on atomic arity assignment for terms **************************)
  21
  22 lemma aaa_da: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ∃d. ⦃G, L⦄ ⊢ T ▪[h, g] d.
  23 #h #g #G #L #T #A #H elim H -G -L -T -A
  24 [ #G #L #k elim (deg_total h g k) /3 width=2 by da_sort, ex_intro/
  25 | * #G #L #K #V #B #i #HLK #_ * /3 width=5 by da_ldef, da_ldec, ex_intro/
  26 | #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by da_bind, ex_intro/
  27 | #a #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by da_bind, ex_intro/
  28 | #G #L #V #T #B #A #_ #_ #_ * /3 width=2 by da_flat, ex_intro/
  29 | #G #L #W #T #A #_ #_ #_ * /3 width=2 by da_flat, ex_intro/
  30 ]
  31 qed-.