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

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  14
  15 include "basic_2/rt_transition/lpx_rdeq.ma".
  16 include "basic_2/rt_computation/lpxs_lpx.ma".
  17
  18 (* UNBOUND PARALLEL RT-COMPUTATION FOR FULL LOCAL ENVIRONMENTS **************)
  19
  20 (* Properties with sort-irrelevant equivalence on referred entries **********)
  21
  22 (* Basic_2A1: uses: lleq_lpxs_trans *)
  23 lemma rdeq_lpxs_trans (h) (G) (T:term):
  24                       ∀L2,K2. ⦃G, L2⦄ ⊢ ⬈*[h] K2 →
  25                       ∀L1. L1 ≛[T] L2 →
  26                       ∃∃K1. ⦃G, L1⦄ ⊢ ⬈*[h] K1 & K1 ≛[T] K2.
  27 #h #G #T #L2 #K2 #H @(lpxs_ind_sn … H) -L2 /2 width=3 by ex2_intro/
  28 #L #L2 #HL2 #_ #IH #L1 #HT
  29 elim (rdeq_lpx_trans … HL2 … HT) -L #L #HL1 #HT
  30 elim (IH … HT) -L2 #K #HLK #HT
  31 /3 width=3 by lpxs_step_sn, ex2_intro/
  32 qed-.
  33
  34 (* Basic_2A1: uses: lpxs_nlleq_inv_step_sn *)
  35 lemma lpxs_rdneq_inv_step_sn (h) (G) (T:term):
  36                              ∀L1,L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → (L1 ≛[T] L2 → ⊥) →
  37                              ∃∃L,L0. ⦃G, L1⦄ ⊢ ⬈[h] L & L1 ≛[T] L → ⊥ &
  38                                      ⦃G, L⦄ ⊢ ⬈*[h] L0 & L0 ≛[T] L2.
  39 #h #G #T #L1 #L2 #H @(lpxs_ind_sn … H) -L1
  40 [ #H elim H -H //
  41 | #L1 #L #H1 #H2 #IH2 #H12 elim (rdeq_dec L1 L T) #H
  42   [ -H1 -H2 elim IH2 -IH2 /3 width=3 by rdeq_trans/ -H12
  43     #L0 #L3 #H1 #H2 #H3 #H4 lapply (rdeq_rdneq_trans … H … H2) -H2
  44     #H2 elim (rdeq_lpx_trans … H1 … H) -L
  45     #L #H1 #H lapply (rdneq_rdeq_div … H … H2) -H2
  46     #H2 elim (rdeq_lpxs_trans … H3 … H) -L0
  47     /3 width=8 by rdeq_trans, ex4_2_intro/
  48   | -H12 -IH2 /3 width=6 by ex4_2_intro/
  49   ]
  50 ]
  51 qed-.