matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
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   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/syntax/ext2_tc.ma".
  16 include "basic_2/relocation/lexs_tc.ma".
  17 include "basic_2/relocation/lex.ma".
  18
  19 (* GENERIC EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS **************)
  20
  21 (* Inversion lemmas with transitive closure *********************************)
  22
  23 lemma s_rs_transitive_lex_inv_isid: ∀R. s_rs_transitive … R (λ_.lex R) →
  24                                     s_rs_transitive_isid cfull (cext2 R).
  25 #R #HR #f #Hf #L2 #T1 #T2 #H #L1 #HL12
  26 elim (ext2_tc … H) -H
  27 [ /3 width=1 by ext2_inv_tc, ext2_unit/
  28 | #I #V1 #V2 #HV12
  29   @ext2_inv_tc @ext2_pair
  30   @(HR … HV12) -HV12 /2 width=3 by ex2_intro/ (**) (* auto fails *)
  31 ]
  32 qed-.