matita/matita/contribs/lambdadelta/basic_2/etc/cpr/cpr_ltpr.etc

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  14
  15 include "basic_2/reducibility/ltpr_tpss.ma".
  16 include "basic_2/reducibility/cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
  19
  20 (* Properties concerning parallel unfold on terms ***************************)
  21
  22 (* Note: we could invoke tpss_weak_full instead of ltpr_fwd_length *)
  23 (* Basic_1: was only: pr2_subst1 *)
  24 lemma cpr_tpss_ltpr: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L2 ⊢ T1 ➡ T2 →
  25                      ∀d,e,U1. L1 ⊢ T1 ▶* [d, e] U1 →
  26                      ∃∃U2. L2 ⊢ U1 ➡ U2 & L2 ⊢ T2 ▶* [d, e] U2.
  27 #L1 #L2 #HL12 #T1 #T2 * #T #HT1 #HT2 #d #e #U1 #HTU1
  28 elim (ltpr_tpr_tpss_conf … HL12 … HT1 … HTU1) -L1 -HT1 #U #HU1 #HTU
  29 elim (tpss_conf_eq … HT2 … HTU) -T /3 width=3/
  30 qed.
  31
  32 lemma cpr_ltpr_conf_eq: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 → ∀L2. L1 ➡ L2 →
  33                         ∃∃T. L2 ⊢ T1 ➡ T & T2 ➡ T.
  34 #L1 #T1 #T2 * #T #HT1 #HT2 #L2 #HL12
  35 >(ltpr_fwd_length … HL12) in HT2; #HT2
  36 elim (ltpr_tpr_tpss_conf … HL12 … HT2) -L1 /3 width=3/
  37 qed.
  38
  39 lemma cpr_ltpr_conf_tpss: ∀L1,L2. L1 ➡ L2 → ∀T1,T2. L1 ⊢ T1 ➡ T2 →
  40                           ∀d,e,U1. L1 ⊢ T1 ▶* [d, e] U1 →
  41                           ∃∃U2. L2 ⊢ U1 ➡ U2 & L2 ⊢ T2 ➡ U2.
  42 #L1 #L2 #HL12 #T1 #T2 #HT12 #d #e #U1 #HTU1
  43 elim (cpr_ltpr_conf_eq … HT12 … HL12) -HT12 #T #HT1 #HT2
  44 elim (cpr_tpss_ltpr … HL12 … HT1 … HTU1) -L1 -HT1 #U2 #HU12 #HTU2
  45 lapply (tpss_weak_full … HTU2) -HTU2 #HTU2 /3 width=5/ (**) (* /4 width=5/ is too slow *)
  46 qed.