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

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  14
  15 include "basic_2/rt_transition/lfpx_lfdeq.ma".
  16 include "basic_2/rt_computation/lfpxs_fqup.ma".
  17
  18 (* UNCOUNTED PARALLEL RT-COMPUTATION FOR LOCAL ENV.S ON REFERRED ENTRIES ****)
  19
  20 (* Properties with degree-based equivalence on referred entries *************)
  21
  22 (* Basic_2A1: was: lleq_lpxs_trans *)
  23 lemma lfdeq_lfpxs_trans: ∀h,o,G,L2,K2,T. ⦃G, L2⦄ ⊢ ⬈*[h, T] K2 →
  24                          ∀L1. L1 ≛[h, o, T] L2 →
  25                          ∃∃K1. ⦃G, L1⦄ ⊢ ⬈*[h, T] K1 & K1 ≛[h, o, T] K2.
  26 #h #o #G #L2 #K2 #T #H @(lfpxs_ind_sn … H) -K2 /2 width=3 by ex2_intro/
  27 #K #K2 #_ #HK2 #IH #L1 #HT elim (IH … HT) -L2
  28 #L #HL1 #HT elim (lfdeq_lfpx_trans … HK2 … HT) -K
  29 /3 width=3 by lfpxs_step_dx, ex2_intro/
  30 qed-.
  31
  32 (* Basic_2A1: was: lpxs_nlleq_inv_step_sn *)
  33 lemma lfpxs_lfdneq_inv_step_sn: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 → (L1 ≛[h, o, T] L2 → ⊥) →
  34                                 ∃∃L,L0. ⦃G, L1⦄ ⊢ ⬈[h, T] L & L1 ≛[h, o, T] L → ⊥ & ⦃G, L⦄ ⊢ ⬈*[h, T] L0 & L0 ≛[h, o, T] L2.
  35 #h #o #G #L1 #L2 #T #H @(lfpxs_ind_dx … H) -L1
  36 [ #H elim H -H //
  37 | #L1 #L #H1 #H2 #IH2 #H12 elim (lfdeq_dec h o L1 L T) #H
  38   [ -H1 -H2 elim IH2 -IH2 /3 width=3 by lfdeq_trans/ -H12
  39     #L0 #L3 #H1 #H2 #H3 #H4 lapply (lfdeq_lfdneq_trans … H … H2) -H2
  40     #H2 elim (lfdeq_lfpx_trans … H1 … H) -L
  41     #L #H1 #H lapply (lfdneq_lfdeq_div … H … H2) -H2
  42     #H2 elim (lfdeq_lfpxs_trans … H3 … H) -L0
  43     /3 width=8 by lfdeq_trans, ex4_2_intro/
  44   | -H12 -IH2 /3 width=6 by ex4_2_intro/
  45   ]
  46 ]
  47 qed-.