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

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  14
  15 include "basic_2/substitution/llpx_sn_ldrop.ma".
  16 include "basic_2/static/ssta.ma".
  17
  18 (* STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS ******************************)
  19
  20 (* Properties on lazy sn pointwise extensions *******************************)
  21
  22 lemma ssta_llpx_sn_conf: ∀R. (∀I,L.reflexive … (R I L)) →
  23                              (∀I.l_liftable (R I)) →
  24                          ∀h,g,G. s_r_confluent1 … (ssta h g G) (llpx_sn R 0).
  25 #R #H1R #H2R #h #g #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
  26 [ /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/
  27 | #G #Ls #Ks #V1s #W2s #V2s #i #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
  28   #Kd #V1d #HLKd #HV1s #HV1sd
  29   lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
  30   lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
  31   @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
  32 | #G #Ls #Ks #V1s #W1s #l #i #HLKs #Hl #HVW1s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
  33   #Kd #V1d #HLKd #HV1s #HV1sd
  34   lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
  35   lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
  36   @(llpx_sn_lift_le … HLKs HLKd … HVW1s) -HLKs -HLKd -HVW1s /2 width=1 by/ (**) (* full auto too slow *)
  37 | #a #I #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
  38   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_bind/
  39 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  40   /3 width=1 by llpx_sn_flat/
  41 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  42   /3 width=1 by llpx_sn_flat/
  43 ]
  44 qed-.