matita/matita/contribs/lambdadelta/basic_2/etc_2A1/llpx/cpxs_llpx.etc

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  14
  15 include "basic_2/reduction/llpx_ldrop.ma".
  16 include "basic_2/computation/cpxs_cpxs.ma".
  17
  18 (* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
  19
  20 (* Properties on lazy sn reduction on local environments ********************)
  21
  22 lemma cpxs_llpx_conf: ∀h,g,G. s_r_confluent1 … (cpxs h g G) (llpx h g G 0).
  23 /3 width=5 by llpx_cpx_conf, s_r_conf1_LTC1/ qed-.
  24
  25 lemma llpx_cpx_trans: ∀h,g,G. s_r_transitive … (cpx h g G) (llpx h g G 0).
  26 #h #g #G #L2 #T1 #T2 #HT12 elim HT12 -G -L2 -T1 -T2
  27 [ /2 width=3 by/
  28 | /3 width=2 by cpx_cpxs, cpx_sort/
  29 | #I #G #L2 #K2 #V0 #V2 #W2 #i #HLK2 #_ #HVW2 #IHV02 #L1 #HL12
  30   elim (llpx_inv_lref_ge_dx … HL12 … HLK2) -L2
  31   /5 width=8 by cpxs_delta, cpxs_strap2, llpx_cpx_conf/
  32 | #a #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
  33   elim (llpx_inv_bind_O … HL12) -HL12 /4 width=1 by cpxs_bind/
  34 | #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #HL12
  35   elim (llpx_inv_flat … HL12) -HL12 /3 width=1 by cpxs_flat/
  36 | #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IHT1 #L1 #HL12
  37   elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_zeta/
  38 | #G #L2 #V2 #T1 #T2 #HT12 #IHT12 #L1 #HL12
  39   elim (llpx_inv_flat … HL12) /3 width=1 by cpxs_tau/
  40 | #G #L2 #V1 #V2 #T2 #HV12 #IHV12 #L1 #HL12
  41   elim (llpx_inv_flat … HL12) /3 width=1 by cpxs_ti/
  42 | #a #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #HL12
  43   elim (llpx_inv_flat … HL12) -HL12 #HV1 #HL12
  44   elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_beta/
  45 | #a #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #HV2 #_ #_ #IHV1 #IHW12 #IHT12 #L1 #HL12
  46   elim (llpx_inv_flat … HL12) -HL12 #HV1 #HL12
  47   elim (llpx_inv_bind_O … HL12) /3 width=3 by cpxs_theta/
  48 ]
  49 qed-.
  50
  51 lemma llpx_cpxs_trans: ∀h,g,G. s_rs_transitive … (cpx h g G) (llpx h g G 0).
  52 #h #g #G @s_r_trans_LTC1 /2 width=3 by llpx_cpx_trans, llpx_cpx_conf/ (**) (* full auto fails here but works in cprs_cprs *)
  53 qed-.