matita/matita/contribs/lambdadelta/static_2/syntax/sd_lt.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 "static_2/syntax/sh_lt.ma".
  16 include "static_2/syntax/sd_d.ma".
  17
  18 (* SORT DEGREE **************************************************************)
  19
  20 (* Properties with sh_lt ****************************************************)
  21
  22 lemma deg_SO_gt (h): sh_lt h →
  23       ∀s1,s2. s1 < s2 → deg_SO h s1 s2 𝟎.
  24 #h #Hh #s1 #s2 #Hs12 @deg_SO_zero
  25 #n @(nat_ind_succ … n) -n
  26 [ <sh_nexts_zero #H destruct
  27   elim (nlt_inv_refl … Hs12)
  28 | #n #_ <sh_nexts_succ #H
  29   lapply (sh_next_lt h Hh (⇡*[h,n]s2)) >H -H #H
  30   lapply (nlt_trans … H … Hs12) -s1 #H1
  31   /3 width=5 by nlt_ge_false, sh_nexts_le/ (* full auto too slow *)
  32 ]
  33 qed.