matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_req.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "static_2/static/req.ma".
  16 include "basic_2/rt_transition/rpx_fsle.ma".
  17
  18 (* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-TRANSITION FOR TERMS ***************)
  19
  20 (* Properties with syntactic equivalence for lenvs on referred entries ******)
  21
  22 (* Basic_2A1: was: lleq_cpx_trans *)
  23 lemma req_cpx_trans: ∀h,G. req_transitive (cpx h G).
  24 #h #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2 /2 width=2 by cpx_ess/
  25 [ #I #G #K2 #V1 #V2 #W2 #_ #IH #HVW2 #L1 #H
  26   elim (req_inv_zero_pair_dx … H) -H #K1 #HK12 #H destruct
  27   /3 width=3 by cpx_delta/
  28 | #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
  29   elim (req_inv_lref_bind_dx … H) -H #I1 #K1 #HK12 #H destruct
  30   /3 width=3 by cpx_lref/
  31 | #p #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
  32   elim (req_inv_bind … H) -H /3 width=1 by cpx_bind/
  33 | #I #G #L2 #V1 #V2 #T1 #T2 #_ #_ #IHV12 #IHT12 #L1 #H
  34   elim (req_inv_flat … H) -H /3 width=1 by cpx_flat/
  35 | #G #L2 #V2 #T1 #T #T2 #_ #HT2 #IH #L1 #H
  36   elim (req_inv_bind … H) -H /3 width=3 by cpx_zeta/
  37 | #G #L2 #W1 #T1 #T2 #_ #IH #L1 #H
  38   elim (req_inv_flat … H) -H /3 width=1 by cpx_eps/
  39 | #G #L2 #W1 #W2 #T1 #_ #IH #L1 #H
  40   elim (req_inv_flat … H) -H /3 width=1 by cpx_ee/
  41 | #p #G #L2 #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV12 #IHW12 #IHT12 #L1 #H
  42   elim (req_inv_flat … H) -H #HV1 #H
  43   elim (req_inv_bind … H) -H /3 width=1 by cpx_beta/
  44 | #p #G #L2 #V1 #V #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #IHV1 #IHW12 #IHT12 #HV2 #L1 #H
  45   elim (req_inv_flat … H) -H #HV1 #H
  46   elim (req_inv_bind … H) -H /3 width=3 by cpx_theta/
  47 ]
  48 qed-.
  49 (*
  50 (* Basic_2A1: was: cpx_lleq_conf *)
  51 lemma cpx_req_conf: ∀h,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈[h] T2 →
  52                     ∀L1. L2 ≘[T1] L1 → ⦃G, L1⦄ ⊢ T1 ⬈[h] T2.
  53 /3 width=3 by req_cpx_trans, req_sym/ qed-.
  54 *)
  55 (* Basic_2A1: was: cpx_lleq_conf_sn *)
  56 lemma cpx_req_conf_sn: ∀h,G. s_r_confluent1 … (cpx h G) req.
  57 /2 width=5 by cpx_rex_conf/ qed-.
  58 (*
  59 (* Basic_2A1: was: cpx_lleq_conf_dx *)
  60 lemma cpx_req_conf_dx: ∀h,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈[h] T2 →
  61                        ∀L1. L1 ≘[T1] L2 → L1 ≘[T2] L2.
  62 /4 width=6 by cpx_req_conf_sn, req_sym/ qed-.
  63 *)