matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_lpr.ma

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  10 (*       \ /        This file is distributed under the terms of the       *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/rt_transition/lpr.ma".
  16 include "basic_2/rt_computation/cpms_cpms.ma".
  17
  18 (* T-BOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
  19
  20 (* Properties concerning sn parallel reduction on local environments ********)
  21
  22 lemma lpr_cpm_trans (n) (h) (G):
  23                     ∀L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ➡[n, h] T2 →
  24                     ∀L1. ⦃G, L1⦄ ⊢ ➡[h] L2 → ⦃G, L1⦄ ⊢ T1 ➡*[n, h] T2.
  25 #n #h #G #L2 #T1 #T2 #H @(cpm_ind … H) -n -G -L2 -T1 -T2
  26 [ /2 width=3 by/
  27 | /3 width=2 by cpm_cpms/
  28 | #n #G #K2 #V2 #V4 #W4 #_ #IH #HVW4 #L1 #H
  29   elim (lpr_inv_pair_dx … H) -H #K1 #V1 #HK12 #HV12 #H destruct
  30   /4 width=3 by cpms_delta, cpms_step_sn/
  31 | #n #G #K2 #V2 #V4 #W4 #_ #IH #HVW4 #L1 #H
  32   elim (lpr_inv_pair_dx … H) -H #K1 #V1 #HK12 #HV12 #H destruct
  33   /4 width=3 by cpms_ell, cpms_step_sn/
  34 | #n #I2 #G #K2 #T #U #i #_ #IH #HTU #L1 #H
  35   elim (lpr_inv_bind_dx … H) -H #I1 #K1 #HK12 #HI12 #H destruct
  36   /4 width=3 by cpms_lref, cpms_step_sn/
  37 | /4 width=1 by cpms_bind, lpr_bind_refl_dx/
  38 | /3 width=1 by cpms_appl/
  39 | /3 width=1 by cpms_cast/
  40 | /4 width=3 by cpms_zeta, lpr_bind_refl_dx/
  41 | /3 width=1 by cpms_eps/
  42 | /3 width=1 by cpms_ee/
  43 | /4 width=1 by lpr_bind_refl_dx, cpms_beta/
  44 | /4 width=3 by lpr_bind_refl_dx, cpms_theta/
  45 ]
  46 qed-.
  47
  48 (*
  49
  50 (* Basic_1: uses: pr3_pr2_pr2_t *)
  51 (* Basic_1: includes: pr3_pr0_pr2_t *)
  52 (* Basic_2A1: includes: lpr_cpr_trans *)
  53 lemma lpr_cpm_trans (n) (h) (G): s_r_transitive … (λL. cpm h G L n) (λ_. lpr h G).
  54
  55 lemma cpr_bind2: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 → ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡ T2 →
  56                  ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
  57 /4 width=5 by lpr_cpr_trans, cprs_bind_dx, lpr_pair/ qed.
  58
  59 (* Advanced properties ******************************************************)
  60
  61 (* Basic_1: was only: pr3_pr2_pr3_t pr3_wcpr0_t *)
  62 lemma lpr_cprs_trans: ∀G. b_rs_transitive … (cpr G) (λ_. lpr G).
  63 #G @b_c_trans_CTC1 /2 width=3 by lpr_cpr_trans/ (**) (* full auto fails *)
  64 qed-.
  65
  66 lemma cprs_bind2_dx: ∀G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ➡ V2 →
  67                      ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ➡* T2 →
  68                      ∀a. ⦃G, L⦄ ⊢ ⓑ{a,I}V1.T1 ➡* ⓑ{a,I}V2.T2.
  69 /4 width=5 by lpr_cprs_trans, cprs_bind_dx, lpr_pair/ qed.
  70 *)