matita/matita/contribs/lambda_delta/basic_2/equivalence/lcpcs_lcprs.ma

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  14
  15 include "basic_2/computation/lcprs.ma".
  16 include "basic_2/equivalence/lcpcs.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON LOCAL ENVIRONMENTS *************)
  19
  20 (* Properties about context sensitive computation on local environments *****)
  21
  22 lemma lcpcs_lcprs_dx: ∀L1,L2. L1 ⊢ ➡* L2 → L1 ⊢ ⬌* L2.
  23 #L1 #L2 #H @(lcprs_ind … H) -L2 /width=1/ /3 width=3/
  24 qed.
  25
  26 lemma lcpcs_lcprs_sn: ∀L1,L2. L2 ⊢ ➡* L1 → L1 ⊢ ⬌* L2.
  27 #L1 #L2 #H @(lcprs_ind_dx … H) -L2 /width=1/ /3 width=3/
  28 qed.
  29
  30 lemma lcpcs_lcprs_strap1: ∀L1,L. L1 ⊢ ⬌* L → ∀L2. L ⊢ ➡* L2 → L1 ⊢ ⬌* L2.
  31 #L1 #L #HL1 #L2 #H @(lcprs_ind … H) -L2 /width=1/ /2 width=3/
  32 qed.
  33
  34 lemma lcpcs_lcprs_strap2: ∀L1,L. L1 ⊢ ➡* L → ∀L2. L ⊢ ⬌* L2 → L1 ⊢ ⬌* L2.
  35 #L1 #L #H #L2 #HL2 @(lcprs_ind_dx … H) -L1 /width=1/ /2 width=3/
  36 qed.
  37
  38 lemma lcpcs_lcprs_div: ∀L1,L. L1 ⊢ ⬌* L → ∀L2. L2 ⊢ ➡* L → L1 ⊢ ⬌* L2.
  39 #L1 #L #HL1 #L2 #H @(lcprs_ind_dx … H) -L2 /width=1/ /2 width=3/
  40 qed.
  41
  42 lemma lcpcs_lcprs_conf: ∀L1,L. L ⊢ ➡* L1 → ∀L2. L ⊢ ⬌* L2 → L1 ⊢ ⬌* L2.
  43 #L1 #L #H #L2 #HL2 @(lcprs_ind … H) -L1 /width=1/ /2 width=3/
  44 qed.
  45
  46 lemma lcprs_div: ∀L1,L. L1 ⊢ ➡* L → ∀L2. L2 ⊢ ➡* L → L1 ⊢ ⬌* L2.
  47 #L1 #L #HL1 #L2 #H @(lcprs_ind_dx … H) -L2 /2 width=1/ /2 width=3/
  48 qed.