matita/matita/contribs/lambda_delta/basic_2/reducibility/crf_append.ma

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   3 (*      ||M||                                                             *)
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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/substitution/ldrop_ldrop.ma".
  16 include "basic_2/reducibility/crf.ma".
  17
  18 (* CONTEXT-SENSITIVE REDUCIBLE TERMS ****************************************)
  19
  20 (* advanced inversion lemmas ************************************************)
  21 (*
  22 lemma crf_inv_labst_last: ∀L1,T,W. L1 ⊢ 𝐑⦃T⦄ → ⇩[0, |L1|-1] L1 ≡ ⋆.ⓛW →
  23                           ∀L2. ⇩[|L1|-1, 1] L1 ≡ L2 → L2 ⊢ 𝐑⦃T⦄.
  24 #L1 #T #W #H elim H -L1 -T /2 width=1/ /3 width=1/
  25 [ #L1 #K1 #V1 #i #HLK1 #HL1 #L2 #HL12 destruct
  26   lapply (ldrop_fwd_ldrop2_length … HLK1) #H
  27   elim (le_to_or_lt_eq i (|L1|-1) ?) /2 width=1/ -H #Hi destruct [ -HL1 | - HL12 ]
  28   [ elim (ldrop_conf_lt … HL12 … HLK1 ?) -HLK1 -HL12 // -Hi /2 width=3/
  29   | lapply (ldrop_mono … HL1 … HLK1) -HL1 -HLK1 #H destruct
  30   ]
  31 | #a #I #L1 #V #T #HI #_
  32   normalize <minus_plus_m_m #IHT #HL1 #L2 #HL12
  33   lapply (ldrop_fwd_ldrop2_length … HL1) #H
  34   lapply (ltn_to_ltO … H) -H #H
  35   @(crf_ib2_dx … HI) @IHT
  36   [ @ldrop_ldrop_lt //
  37   | @ldrop_skip_lt //
  38 ]
  39 qed.
  40
  41
  42 lemma crf_inv_labst_last: ∀L,T,W. ⋆.ⓛW @@ L ⊢ 𝐑⦃T⦄  → L ⊢ 𝐑⦃T⦄.
  43 #L2 #T #H elim H -L2 -T
  44 [ #L2 #K2 #V2 #i #HLK2 #L1 #HL12
  45 *)