matita/matita/contribs/lambdadelta/basic_2A/multiple/llpx_sn_lpx_sn.ma

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  14
  15 include "basic_2A/substitution/lpx_sn_drop.ma".
  16 include "basic_2A/multiple/llpx_sn.ma".
  17
  18 (* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
  19
  20 (* Properties on pointwise extensions ***************************************)
  21
  22 lemma lpx_sn_llpx_sn: ∀R. (∀L. reflexive … (R L)) →
  23                       ∀T,L1,L2,l. lpx_sn R L1 L2 → llpx_sn R l T L1 L2.
  24 #R #HR #T #L1 @(f2_ind … rfw … L1 T) -L1 -T
  25 #x #IH #L1 * *
  26 [ -HR -IH /4 width=2 by lpx_sn_fwd_length, llpx_sn_sort/
  27 | -HR #i elim (lt_or_ge i (|L1|))
  28   [2: -IH /4 width=4 by lpx_sn_fwd_length, llpx_sn_free, le_repl_sn_conf_aux/ ]
  29   #Hi #Hx #L2 #l elim (ylt_split i l)
  30   [ -x /3 width=2 by llpx_sn_skip, lpx_sn_fwd_length/ ]
  31   #Hli #HL12 elim (drop_O1_lt (Ⓕ) L1 i) //
  32   #I #K1 #V1 #HLK1 elim (lpx_sn_drop_conf … HL12 … HLK1) -HL12
  33   /4 width=9 by llpx_sn_lref, drop_fwd_rfw/
  34 | -HR -IH /4 width=2 by lpx_sn_fwd_length, llpx_sn_gref/
  35 | /4 width=1 by llpx_sn_bind, lpx_sn_pair/
  36 | -HR /3 width=1 by llpx_sn_flat/
  37 ]
  38 qed.