matita/matita/contribs/lambdadelta/basic_2/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_2/static/da_lift.ma".
  16
  17 (* DEGREE ASSIGNMENT FOR TERMS **********************************************)
  18
  19 (* Main properties **********************************************************)
  20
  21 theorem da_mono: ∀h,g,G,L,T,l1. ⦃G, L⦄ ⊢ T ▪[h, g] l1 →
  22                  ∀l2. ⦃G, L⦄ ⊢ T ▪[h, g] l2 → l1 = l2.
  23 #h #g #G #L #T #l1 #H elim H -G -L -T -l1
  24 [ #G #L #k #l1 #Hkl1 #l2 #H
  25   lapply (da_inv_sort … H) -G -L #Hkl2
  26   >(deg_mono … Hkl2 … Hkl1) -h -k -l2 //
  27 | #G #L #K #V #i #l1 #HLK #_ #IHV #l2 #H
  28   elim (da_inv_lref … H) -H * #K0 #V0 [| #l0 ] #HLK0 #HV0 [| #Hl0 ]
  29   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /2 width=1/
  30 | #G #L #K #W #i #l1 #HLK #_ #IHW #l2 #H
  31   elim (da_inv_lref … H) -H * #K0 #W0 [| #l0 ] #HLK0 #HW0 [| #Hl0 ]
  32   lapply (ldrop_mono … HLK0 … HLK) -HLK -HLK0 #H destruct /3 width=1/
  33 | #a #I #G #L #V #T #l1 #_ #IHT #l2 #H
  34   lapply (da_inv_bind … H) -H /2 width=1/
  35 | #I #G #L #V #T #l1 #_ #IHT #l2 #H
  36   lapply (da_inv_flat … H) -H /2 width=1/
  37 ]
  38 qed-.