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

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  14
  15 include "basic_2/rt_transition/lpx_reqx.ma".
  16 include "basic_2/rt_computation/lpxs_lpx.ma".
  17
  18 (* EXTENDED 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 reqx_lpxs_trans (G) (T:term):
  24       ∀L2,K2. ❪G,L2❫ ⊢ ⬈* K2 → ∀L1. L1 ≛[T] L2 →
  25       ∃∃K1. ❪G,L1❫ ⊢ ⬈* K1 & K1 ≛[T] K2.
  26 #G #T #L2 #K2 #H @(lpxs_ind_sn … H) -L2 /2 width=3 by ex2_intro/
  27 #L #L2 #HL2 #_ #IH #L1 #HT
  28 elim (reqx_lpx_trans … HL2 … HT) -L #L #HL1 #HT
  29 elim (IH … HT) -L2 #K #HLK #HT
  30 /3 width=3 by lpxs_step_sn, ex2_intro/
  31 qed-.
  32
  33 (* Basic_2A1: uses: lpxs_nlleq_inv_step_sn *)
  34 lemma lpxs_rneqx_inv_step_sn (G) (T:term):
  35       ∀L1,L2. ❪G,L1❫ ⊢ ⬈* L2 → (L1 ≛[T] L2 → ⊥) →
  36       ∃∃L,L0. ❪G,L1❫ ⊢ ⬈ L & L1 ≛[T] L → ⊥ & ❪G,L❫ ⊢ ⬈* L0 & L0 ≛[T] L2.
  37 #G #T #L1 #L2 #H @(lpxs_ind_sn … H) -L1
  38 [ #H elim H -H //
  39 | #L1 #L #H1 #H2 #IH2 #H12 elim (reqx_dec L1 L T) #H
  40   [ -H1 -H2 elim IH2 -IH2 /3 width=3 by reqx_trans/ -H12
  41     #L0 #L3 #H1 #H2 #H3 #H4 lapply (reqx_rneqx_trans … H … H2) -H2
  42     #H2 elim (reqx_lpx_trans … H1 … H) -L
  43     #L #H1 #H lapply (rneqx_reqx_div … H … H2) -H2
  44     #H2 elim (reqx_lpxs_trans … H3 … H) -L0
  45     /3 width=8 by reqx_trans, ex4_2_intro/
  46   | -H12 -IH2 /3 width=6 by ex4_2_intro/
  47   ]
  48 ]
  49 qed-.