matita/matita/contribs/lambdadelta/basic_2/reduction/cpx_llpx_sn.ma

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  14
  15 include "basic_2/relocation/llpx_sn_ldrop.ma".
  16 include "basic_2/reduction/cpx.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL REDUCTION FOR TERMS ******************)
  19
  20 (* Properties on lazy sn pointwise extensions *******************************)
  21
  22 (* Note: lemma 1000 *)
  23 lemma llpx_sn_cpx_conf: ∀R. (∀L. reflexive … (R L)) → l_liftable R → l_deliftable_sn R →
  24                         ∀h,g,G,Ls,T1,T2. ⦃G, Ls⦄ ⊢ T1 ➡[h, g] T2 →
  25                         ∀Ld. llpx_sn R 0 T1 Ls Ld → llpx_sn R 0 T2 Ls Ld.
  26 #R #H1R #H2R #H3R #h #g #G #Ls #T1 #T2 #H elim H -G -Ls -T1 -T2
  27 [ //
  28 | /3 width=4 by llpx_sn_fwd_length, llpx_sn_sort/
  29 | #I #G #Ls #Ks #V1s #V2s #W2s #i #HLKs #_ #HVW2s #IHV12s #Ld #H elim (llpx_sn_inv_lref_ge_sn … H … HLKs) // -H
  30   #Kd #V1d #HLKd #HV1s #HV1sd
  31   lapply (ldrop_fwd_drop2 … HLKs) -HLKs #HLKs
  32   lapply (ldrop_fwd_drop2 … HLKd) -HLKd #HLKd
  33   @(llpx_sn_lift_le … HLKs HLKd … HVW2s) -HLKs -HLKd -HVW2s /2 width=1 by/ (**) (* full auto too slow *)
  34 | #a #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
  35   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_bind/
  36 | #I #G #Ls #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  37   /3 width=1 by llpx_sn_flat/
  38 | #G #Ls #V #T1 #T2 #T #_ #HT2 #IHT12 #Ld #H elim (llpx_sn_inv_bind_O … H) -H
  39   /3 width=10 by llpx_sn_inv_lift_le, ldrop_drop/
  40 | #G #Ls #V #T1 #T2 #_ #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H /2 width=1 by/
  41 | #G #Ls #V1 #V2 #T #_ #IHV12 #Ld #H elim (llpx_sn_inv_flat … H) -H /2 width=1 by/
  42 | #a #G #Ls #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  43   #HV1 #H elim (llpx_sn_inv_bind_O … H) -H
  44   /4 width=5 by llpx_sn_bind_repl_SO, llpx_sn_flat, llpx_sn_bind/
  45 | #a #G #Ls #V1 #V2 #V #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV12 #IHW12 #IHT12 #Ld #H elim (llpx_sn_inv_flat … H) -H
  46   #HV1 #H elim (llpx_sn_inv_bind_O … H) -H //
  47   #HW1 #HT1 @llpx_sn_bind_O /2 width=1 by/ @llpx_sn_flat (**) (* full auto too slow *)
  48   [ /3 width=10 by llpx_sn_lift_le, ldrop_drop/
  49   | /3 width=4 by llpx_sn_bind_repl_O/
  50 ]
  51 qed-.