matita/matita/contribs/lambdadelta/basic_2/etc_new/llpx_sn/llpx_sn.etc

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  14
  15 include "ground_2/ynat/ynat_plus.ma".
  16 include "basic_2/substitution/drop.ma".
  17
  18 (* LAZY SN POINTWISE EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS ****)
  19
  20 | llpx_sn_lref: ∀I,L1,L2,K1,K2,V1,V2,l,i. l ≤ yinj i →
  21                 ⬇[i] L1 ≡ K1.ⓑ{I}V1 → ⬇[i] L2 ≡ K2.ⓑ{I}V2 →
  22                 llpx_sn R (yinj 0) V1 K1 K2 → R K1 V1 V2 → llpx_sn R l (#i) L1 L2
  23
  24 (* Basic forward lemmas *****************************************************)
  25
  26 lemma llpx_sn_fwd_drop_sn: ∀R,L1,L2,T,l. llpx_sn R l T L1 L2 →
  27                             ∀K1,i. ⬇[i] L1 ≡ K1 → ∃K2. ⬇[i] L2 ≡ K2.
  28 #R #L1 #L2 #T #l #H #K1 #i #HLK1 lapply (llpx_sn_fwd_length … H) -H
  29 #HL12 lapply (drop_fwd_length_le2 … HLK1) -HLK1 /2 width=1 by drop_O1_le/
  30 qed-.
  31
  32 lemma llpx_sn_fwd_drop_dx: ∀R,L1,L2,T,l. llpx_sn R l T L1 L2 →
  33                             ∀K2,i. ⬇[i] L2 ≡ K2 → ∃K1. ⬇[i] L1 ≡ K1.
  34 #R #L1 #L2 #T #l #H #K2 #i #HLK2 lapply (llpx_sn_fwd_length … H) -H
  35 #HL12 lapply (drop_fwd_length_le2 … HLK2) -HLK2 /2 width=1 by drop_O1_le/
  36 qed-.
  37
  38 lemma llpx_sn_fwd_lref: ∀R,L1,L2,l,i. llpx_sn R l (#i) L1 L2 →
  39                         ∨∨ |L1| ≤ i ∧ |L2| ≤ i
  40                          | yinj i < l
  41                          | ∃∃I,K1,K2,V1,V2. ⬇[i] L1 ≡ K1.ⓑ{I}V1 &
  42                                             ⬇[i] L2 ≡ K2.ⓑ{I}V2 &
  43                                             llpx_sn R (yinj 0) V1 K1 K2 &
  44                                             R K1 V1 V2 & l ≤ yinj i.
  45 /2 width=3 by llpx_sn_fwd_lref_aux/ qed-.