matita/matita/contribs/lambdadelta/basic_2A/etc/lpx_sn/cpr_llpx_sn.etc

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  14
  15 include "basic_2/substitution/llpx_sn_ldrop.ma".
  16 include "basic_2/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. (∀I,L.reflexive … (R I L)) →
  23                             (∀I.l_liftable (R I)) →
  24                             (∀I.l_deliftable_sn (R I)) →
  25                         ∀G. s_r_confluent1 … (cpr G) (llpx_sn R 0).
  26 #R #H1R #H2R #H3R #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
  27 [ //
  28 | #G #Ls #Ks #V1s #V2s #W2s #i #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
  29   #Kd #V1d #HLKd #HV1s #HV1sd
  30   lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
  31   lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
  32   @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
  33 | #a #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
  34   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_bind/
  35 | #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  36   /3 width=1 by llpx_sn_flat/
  37 | #G #Ls #V #T1 #T2 #T #_ #HT2 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
  38   /3 width=10 by llpx_sn_inv_lift_le, ldrop_drop/
  39 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H /2 width=1 by/
  40 | #a #G #Ls #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  41   #HV1 #H elim (llpx_sn_inv_bind_O … H) -H
  42   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_flat, llpx_sn_bind/
  43 | #a #G #Ls #V1 #V2 #V #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  44   #HV1 #H elim (llpx_sn_inv_bind_O … H) -H //
  45   #HW1 #HT1 @llpx_sn_bind_O /2 width=1 by/ @llpx_sn_flat (**) (* full auto too slow *)
  46   [ /3 width=10 by llpx_sn_lift_le, ldrop_drop/
  47   | /3 width=4 by llpx_sn_bind_repl_O/
  48 ]
  49 qed-.