matita/matita/contribs/lambdadelta/basic_2A/reduction/cpr_llpx_sn.ma

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  14
  15 include "basic_2A/multiple/llpx_sn_drop.ma".
  16 include "basic_2A/reduction/cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
  19
  20 (* Properties on lazy sn pointwise extensions *******************************)
  21
  22 lemma cpr_llpx_sn_conf: ∀R. (∀L. reflexive … (R L)) → d_liftable R → d_deliftable_sn R →
  23                         ∀G. s_r_confluent1 … (cpr G) (llpx_sn R 0).
  24 #R #H1R #H2R #H3R #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
  25 [ //
  26 | #G #Ls #Ks #V1s #V2s #W2s #i #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
  27   #Kd #V1l #HLKd #HV1s #HV1sd
  28   lapply (drop_fwd_drop2 … HLKs) -HLKs #HLKs
  29   lapply (drop_fwd_drop2 … HLKd) -HLKd #HLKd
  30   @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
  31 | #a #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
  32   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_bind/
  33 | #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  34   /3 width=1 by llpx_sn_flat/
  35 | #G #Ls #V #T1 #T2 #T #_ #HT2 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
  36   /3 width=10 by llpx_sn_inv_lift_le, drop_drop/
  37 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H /2 width=1 by/
  38 | #a #G #Ls #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  39   #HV1 #H elim (llpx_sn_inv_bind_O … H) -H
  40   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_flat, llpx_sn_bind/
  41 | #a #G #Ls #V1 #V2 #V #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  42   #HV1 #H elim (llpx_sn_inv_bind_O … H) -H //
  43   #HW1 #HT1 @llpx_sn_bind_O /2 width=1 by/ @llpx_sn_flat (**) (* full auto too slow *)
  44   [ /3 width=10 by llpx_sn_lift_le, drop_drop/
  45   | /3 width=4 by llpx_sn_bind_repl_O/
  46 ]
  47 qed-.