matita/matita/contribs/lambdadelta/basic_2/reduction/crx_append.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/relocation/ldrop_append.ma".
  16 include "basic_2/reduction/crx.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED REDUCIBLE TERMS *******************************)
  19
  20 (* Advanved properties ******************************************************)
  21
  22 lemma crx_append_sn: ∀h,g,L,K,T. ⦃h, L⦄ ⊢ 𝐑[g]⦃T⦄  → ⦃h, K @@ L⦄ ⊢ 𝐑[g]⦃T⦄.
  23 #h #g #L #K0 #T #H elim H -L -T /2 width=1/ /2 width=2/
  24 #I #L #K #V #i #HLK
  25 lapply (ldrop_fwd_length_lt2 … HLK) #Hi
  26 lapply (ldrop_O1_append_sn_le … HLK … K0) -HLK /2 width=2/ -Hi /2 width=4/
  27 qed.
  28
  29 lemma trx_crx: ∀h,g,L,T. ⦃h, ⋆⦄ ⊢ 𝐑[g]⦃T⦄ → ⦃h, L⦄ ⊢ 𝐑[g]⦃T⦄.
  30 #h #g #L #T #H lapply (crx_append_sn … H) //
  31 qed.