matita/matita/contribs/lambdadelta/basic_2A/static/aaa_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/substitution/drop_drop.ma".
  16 include "basic_2A/static/aaa.ma".
  17
  18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem aaa_mono: ∀G,L,T,A1. ⦃G, L⦄ ⊢ T ⁝ A1 → ∀A2. ⦃G, L⦄ ⊢ T ⁝ A2 → A1 = A2.
  23 #G #L #T #A1 #H elim H -G -L -T -A1
  24 [ #G #L #k #A2 #H
  25   >(aaa_inv_sort … H) -H //
  26 | #I1 #G #L #K1 #V1 #B #i #HLK1 #_ #IHA1 #A2 #H
  27   elim (aaa_inv_lref … H) -H #I2 #K2 #V2 #HLK2 #HA2
  28   lapply (drop_mono … HLK1 … HLK2) -L #H destruct /2 width=1 by/
  29 | #a #G #L #V #T #B1 #A1 #_ #_ #_ #IHA1 #A2 #H
  30   elim (aaa_inv_abbr … H) -H /2 width=1 by/
  31 | #a #G #L #V1 #T1 #B1 #A1 #_ #_ #IHB1 #IHA1 #X #H
  32   elim (aaa_inv_abst … H) -H #B2 #A2 #HB2 #HA2 #H destruct /3 width=1 by eq_f2/
  33 | #G #L #V1 #T1 #B1 #A1 #_ #_ #_ #IHA1 #A2 #H
  34   elim (aaa_inv_appl … H) -H #B2 #_ #HA2
  35   lapply (IHA1 … HA2) -L #H destruct //
  36 | #G #L #V #T #A1 #_ #_ #_ #IHA1 #A2 #H
  37   elim (aaa_inv_cast … H) -H /2 width=1 by/
  38 ]
  39 qed-.