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

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  14
  15 include "basic_2/computation/lfprs.ma".
  16 include "basic_2/equivalence/lfpcs.ma".
  17
  18 (* FOCALIZED PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *********************)
  19
  20 (* Properties on focalized computation for local environments ***************)
  21
  22 lemma lfpcs_lfprs_dx: ∀L1,L2. ⦃L1⦄ ➡* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  23 #L1 #L2 #H @(lfprs_ind … H) -L2 /width=1/ /3 width=3/
  24 qed.
  25
  26 lemma lfpcs_lfprs_sn: ∀L1,L2. ⦃L2⦄ ➡* ⦃L1⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  27 #L1 #L2 #H @(lfprs_ind_dx … H) -L2 /width=1/ /3 width=3/
  28 qed.
  29
  30 lemma lfpcs_lfprs_strap1: ∀L1,L. ⦃L1⦄ ⬌* ⦃L⦄ → ∀L2. ⦃L⦄ ➡* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  31 #L1 #L #HL1 #L2 #H @(lfprs_ind … H) -L2 /width=1/ /2 width=3/
  32 qed.
  33
  34 lemma lfpcs_lfprs_strap2: ∀L1,L. ⦃L1⦄ ➡* ⦃L⦄ → ∀L2. ⦃L⦄ ⬌* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  35 #L1 #L #H #L2 #HL2 @(lfprs_ind_dx … H) -L1 /width=1/ /2 width=3/
  36 qed.
  37
  38 lemma lfpcs_lfprs_div: ∀L1,L. ⦃L1⦄ ⬌* ⦃L⦄ → ∀L2. ⦃L2⦄ ➡* ⦃L⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  39 #L1 #L #HL1 #L2 #H @(lfprs_ind_dx … H) -L2 /width=1/ /2 width=3/
  40 qed.
  41
  42 lemma lfpcs_lfprs_conf: ∀L1,L. ⦃L⦄ ➡* ⦃L1⦄ → ∀L2. ⦃L⦄ ⬌* ⦃L2⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  43 #L1 #L #H #L2 #HL2 @(lfprs_ind … H) -L1 /width=1/ /2 width=3/
  44 qed.
  45
  46 lemma lfprs_div: ∀L1,L. ⦃L1⦄ ➡* ⦃L⦄ → ∀L2. ⦃L2⦄ ➡* ⦃L⦄ → ⦃L1⦄ ⬌* ⦃L2⦄.
  47 #L1 #L #HL1 #L2 #H @(lfprs_ind_dx … H) -L2 /2 width=1/ /2 width=3/
  48 qed.