matita/matita/contribs/lambdadelta/basic_2A/unfold/lstas_llpx_sn.ma

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  14
  15 include "basic_2A/multiple/llpx_sn_drop.ma".
  16 include "basic_2A/unfold/lstas.ma".
  17
  18 (* NAT-ITERATED STATIC TYPE ASSIGNMENT FOR TERMS ****************************)
  19
  20 (* Properties on lazy sn pointwise extensions *******************************)
  21
  22 lemma lstas_llpx_sn_conf: ∀R. (∀L. reflexive … (R L)) → d_liftable R →
  23                           ∀h,G,d. s_r_confluent1 … (lstas h d G) (llpx_sn R 0).
  24 #R #H1R #H2R #h #G #d #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2 -d
  25 [ /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/
  26 | #G #Ls #Ks #V1s #V2s #W2s #i #d #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 | //
  32 | #G #Ls #Ks #V1s #V2s #W2s #i #d #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
  33   #Kd #V1l #HLKd #HV1s #HV1sd
  34   lapply (drop_fwd_drop2 … HLKs) -HLKs #HLKs
  35   lapply (drop_fwd_drop2 … HLKd) -HLKd #HLKd
  36   @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
  37 | #a #I #G #Ls #V #T1 #T2 #d #_ #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 #d #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  40   /3 width=1 by llpx_sn_flat/
  41 | #G #Ls #V #T1 #T2 #d #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  42   /3 width=1 by llpx_sn_flat/
  43 ]
  44 qed-.