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

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  14
  15 include "basic_2/rt_transition/lfpx_fqup.ma".
  16 include "basic_2/rt_transition/lfpx_cpx.ma".
  17 include "basic_2/rt_computation/cpxs_drops.ma".
  18 include "basic_2/rt_computation/cpxs_cpxs.ma".
  19
  20 (* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
  21
  22 (* Properties with uncounted parallel rt-transition on referred entries *****)
  23
  24 lemma lfpx_cpxs_conf: ∀h,G. s_r_confluent1 … (cpxs h G) (lfpx h G).
  25 /3 width=5 by lfpx_cpx_conf, s_r_conf1_LTC1/ qed-.
  26
  27 lemma lfpx_cpx_trans: ∀h,G. s_r_transitive … (cpx h G) (lfpx h G).
  28 #h #G #L2 #T1 #T2 #H @(cpx_ind … H) -G -L2 -T1 -T2 //
  29 [ #G #L2 #s1 #L1 #H elim (lfpx_inv_sort … H) -H * /2 width=1 by cpx_cpxs/
  30 | #I #G #L2 #V #V2 #W2 #_ #IH #HVW2 #Y1 #H
  31   elim (lfpx_inv_zero_pair_dx … H) -H #L1 #V1 #HL1 #HV1 #H destruct
  32   /5 width=3 by lfpx_cpx_conf, cpxs_delta, cpxs_strap2/
  33 | #I2 #G #L2 #V2 #W2 #i #_ #IH #HVW2 #Y1 #H
  34   elim (lfpx_inv_lref_bind_dx … H) -H #I1 #L1 #HL1 #H destruct
  35   /4 width=3 by cpxs_lref, cpxs_strap2/
  36 | #p #I #G #L2 #V #V2 #T #T2 #_ #_ #IHV #IHT #L1 #H
  37   elim (lfpx_inv_bind … H) -H /3 width=1 by cpxs_bind/
  38 | #I #G #L2 #V #V2 #T #T2 #_ #_ #IHV #IHT #L1 #H
  39   elim (lfpx_inv_flat … H) -H /3 width=1 by cpxs_flat/
  40 | #G #L2 #V #T #T2 #T0 #_ #IH #HT02 #L1 #H
  41   elim (lfpx_inv_bind … H) -H /3 width=3 by cpxs_zeta/
  42 | #G #L2 #V #T #T2 #_ #IH #L1 #H
  43   elim (lfpx_inv_flat … H) -H /3 width=1 by cpxs_eps/
  44 | #G #L2 #V #V2 #T #_ #IH #L1 #H
  45   elim (lfpx_inv_flat … H) -H /3 width=1 by cpxs_ee/
  46 | #p #G #L2 #V #V2 #W #W2 #T #T2 #_ #_ #_ #IHV #IHW #IHT #L1 #H
  47   elim (lfpx_inv_flat … H) -H #HV #H
  48   elim (lfpx_inv_bind … H) -H /3 width=1 by cpxs_beta/
  49 | #p #G #L2 #V #V2 #V0 #W #W2 #T #T2 #_ #_ #_ #IHV #IHW #IHT #HV20 #L1 #H
  50   elim (lfpx_inv_flat … H) -H #HV #H
  51   elim (lfpx_inv_bind … H) -H /3 width=3 by cpxs_theta/
  52 ]
  53 qed.
  54
  55 lemma lfpx_cpxs_trans: ∀h,G. s_rs_transitive … (cpx h G) (lfpx h G).
  56 /3 width=6 by lfpx_cpx_conf, lfpx_cpx_trans, s_r_trans_LTC1/
  57 qed-.
  58
  59 (* Advanced properties ******************************************************)
  60
  61 lemma cpx_bind2: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
  62                  ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈[h] T2 →
  63                  ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
  64 /4 width=5 by lfpx_cpx_trans, cpxs_bind_dx, lfpx_pair_refl/ qed.
  65
  66 lemma cpxs_bind2_dx: ∀h,G,L,V1,V2. ⦃G, L⦄ ⊢ V1 ⬈[h] V2 →
  67                      ∀I,T1,T2. ⦃G, L.ⓑ{I}V2⦄ ⊢ T1 ⬈*[h] T2 →
  68                      ∀p. ⦃G, L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
  69 /4 width=5 by lfpx_cpxs_trans, cpxs_bind_dx, lfpx_pair_refl/ qed.