matita/matita/contribs/lambdadelta/basic_2A/static/da_da.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/da_lift.ma".
  16
  17 (* DEGREE ASSIGNMENT FOR TERMS **********************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem da_mono: ∀h,g,G,L,T,d1. ⦃G, L⦄ ⊢ T ▪[h, g] d1 →
  22                  ∀d2. ⦃G, L⦄ ⊢ T ▪[h, g] d2 → d1 = d2.
  23 #h #g #G #L #T #d1 #H elim H -G -L -T -d1
  24 [ #G #L #k #d1 #Hkd1 #d2 #H
  25   lapply (da_inv_sort … H) -G -L #Hkd2
  26   >(deg_mono … Hkd2 … Hkd1) -h -k -d2 //
  27 | #G #L #K #V #i #d1 #HLK #_ #IHV #d2 #H
  28   elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0 #HV0 [| #Hd0 ]
  29   lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /2 width=1 by/
  30 | #G #L #K #W #i #d1 #HLK #_ #IHW #d2 #H
  31   elim (da_inv_lref … H) -H * #K0 #W0 [| #d0 ] #HLK0 #HW0 [| #Hd0 ]
  32   lapply (drop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /3 width=1 by eq_f/
  33 | #a #I #G #L #V #T #d1 #_ #IHT #d2 #H
  34   lapply (da_inv_bind … H) -H /2 width=1 by/
  35 | #I #G #L #V #T #d1 #_ #IHT #d2 #H
  36   lapply (da_inv_flat … H) -H /2 width=1 by/
  37 ]
  38 qed-.