matita/matita/contribs/lambdadelta/basic_2/etc/append/crx_append.etc

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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/relocation/ldrop_append.ma".
  16 include "basic_2/reduction/crx.ma".
  17
  18 (* REDUCIBLE TERMS FOR CONTEXT-SENSITIVE EXTENDED REDUCTION *****************)
  19
  20 (* Advanved properties ******************************************************)
  21
  22 lemma crx_append_sn: ∀h,g,G,L,K,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄  → ⦃G, K @@ L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄.
  23 #h #g #G #L #K0 #T #H elim H -L -T
  24 /2 width=2 by crx_sort, crx_appl_sn, crx_appl_dx, crx_ri2, crx_ib2_sn, crx_ib2_dx, crx_beta, crx_theta/
  25 #I #L #K #V #i #HLK
  26 lapply (ldrop_fwd_length_lt2 … HLK) #Hi
  27 lapply (ldrop_O1_append_sn_le … HLK … K0) -HLK /2 width=4 by crx_delta, lt_to_le/
  28 qed.
  29
  30 lemma trx_crx: ∀h,g,G,L,T. ⦃G, ⋆⦄ ⊢ ➡[h, g] 𝐑⦃T⦄ → ⦃G, L⦄ ⊢ ➡[h, g] 𝐑⦃T⦄.
  31 #h #g #G #L #T #H lapply (crx_append_sn … H) //
  32 qed.