matita/matita/contribs/lambdadelta/basic_2A/etc/lpc/lfpcs_fpcs.etc

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  14
  15 include "basic_2/computation/fprs_cprs.ma".
  16 include "basic_2/computation/lfprs_fprs.ma".
  17 include "basic_2/equivalence/fpcs_fpcs.ma".
  18 include "basic_2/equivalence/lfpcs_lfpcs.ma".
  19
  20 (* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
  21
  22 (* Inversion lemmas on context-free parallel equivalence for closures *******)
  23
  24 lemma lfpcs_inv_fpcs: ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ → ∀T. ⦃L1, T⦄ ⬌* ⦃L2, T⦄.
  25 #L1 #L2 #HL12 #T
  26 elim (lfpcs_inv_lfprs … HL12) -HL12 #L #HL1 #HL2
  27 lapply (lfprs_inv_fprs … HL1 T) -HL1
  28 lapply (lfprs_inv_fprs … HL2 T) -HL2 /2 width=4/
  29 qed-.
  30
  31 (* Properties on context-free parallel equivalence for closures *************)
  32
  33 lemma fpcs_lfpcs: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  34 #L1 #L2 #T1 #T2 #HT12
  35 elim (fpcs_inv_fprs … HT12) -HT12 /3 width=5 by fprs_lfprs, lfprs_div/ (**) (* auto too slow without trace *)
  36 qed.
  37
  38 lemma fpcs_lift: ∀K1,K2,T1,T2. ⦃K1, T1⦄ ⬌* ⦃K2, T2⦄ →
  39                  ∀L1,L2. ⦃L1⦄ ⬌* ⦃L2⦄ →
  40                  ∀d,e. ⇩[d, e] L1 ≡ K1 → ⇩[d, e] L2 ≡ K2 →
  41                  ∀U1,U2. ⇧[d, e] T1 ≡ U1 → ⇧[d, e] T2 ≡ U2 →
  42                  ⦃L1, U1⦄ ⬌* ⦃L2, U2⦄.
  43 #K1 #K2 #T1 #T2 #HT12 #L1 #L2 #HL12 #d #e #HLK1 #HLK2 #U1 #U2 #HTU1 #HTU2
  44 elim (fpcs_inv_fprs … HT12) -HT12 #K #T #HT1 #HT2
  45 elim (lift_total T d e) #U #HTU
  46 elim (fprs_lift … HT1 … HLK1 … HTU1 HTU) -K1 -T1 #K1 #HU1 #_
  47 elim (fprs_lift … HT2 … HLK2 … HTU2 HTU) -K2 -T2 -T #K2 #HU2 #_ -K -d -e
  48 lapply (lfpcs_lfprs_conf K1 … HL12) -HL12 /2 width=3/ #H
  49 lapply (lfpcs_lfprs_strap1 … H K2 ?) -H /2 width=3/ #HK12
  50 lapply (lfpcs_inv_fpcs … HK12 U) -HK12 #HU
  51 /3 width=4 by fpcs_fprs_strap2, fpcs_fprs_div/
  52 qed.