matita/matita/contribs/lambdadelta/basic_2/etc/teqx/cpx_req.etc

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  14
  15 include "static_2/static/req_length.ma".
  16 include "static_2/static/req_drops.ma".
  17 include "basic_2/rt_transition/rpx_fsle.ma".
  18
  19 (* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS **************)
  20
  21 (* Properties with syntactic equivalence for lenvs on referred entries ******)
  22
  23 (* Basic_2A1: was: lleq_cpx_trans *)
  24 lemma req_cpx_trans (G): R_transitive_req (cpx G).
  25 #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2 /2 width=2 by cpx_qu/
  26 [ #I #G #K2 #V1 #V2 #W2 #_ #IH #HVW2 #L1 #H
  27   elim (req_inv_zero_pair_dx … H) -H #K1 #HK12 #H destruct
  28   /3 width=3 by cpx_delta/
  29 | #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
  30   elim (req_inv_lref_bind_dx … H) -H #I1 #K1 #HK12 #H destruct
  31   /3 width=3 by cpx_lref/
  32 | #p #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
  33   elim (req_inv_bind … H) -H /3 width=1 by cpx_bind/
  34 | #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
  35   elim (req_inv_flat … H) -H /3 width=1 by cpx_flat/
  36 | #G #L2 #V2 #T1 #T #T2 #HT1 #_ #IH #L1 #H
  37   elim (req_inv_bind … H) -H #HV2 #H
  38   lapply (req_inv_lifts_bi … H (Ⓣ) … HT1) -H [6:|*: /3 width=2 by drops_refl, drops_drop/ ] #HT
  39   /3 width=3 by cpx_zeta/
  40 | #G #L2 #W1 #T1 #T2 #_ #IH #L1 #H
  41   elim (req_inv_flat … H) -H /3 width=1 by cpx_eps/
  42 | #G #L2 #W1 #W2 #T1 #_ #IH #L1 #H
  43   elim (req_inv_flat … H) -H /3 width=1 by cpx_ee/
  44 | #p #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H
  45   elim (req_inv_flat … H) -H #HV1 #H
  46   elim (req_inv_bind … H) -H /3 width=1 by cpx_beta/
  47 | #p #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV1 #IHW12 #IHT12 #HV2 #L1 #H
  48   elim (req_inv_flat … H) -H #HV1 #H
  49   elim (req_inv_bind … H) -H /3 width=3 by cpx_theta/
  50 ]
  51 qed-.
  52
  53 lemma cpx_req_conf (G): R_confluent1_rex (cpx G) ceq.
  54 /3 width=3 by req_cpx_trans, req_sym/ qed-.
  55
  56 (* Basic_2A1: was: cpx_lleq_conf_sn *)
  57 lemma cpx_req_conf_sn (G): s_r_confluent1 … (cpx G) req.
  58 /2 width=5 by cpx_rex_conf_sn/ qed-.