matita/matita/contribs/lambda_delta/basic_2/computation/lcprs_aaa.ma

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  14
  15 include "basic_2/reducibility/lcpr_aaa.ma".
  16 include "basic_2/computation/cprs.ma".
  17 include "basic_2/computation/lcprs.ma".
  18
  19 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
  20
  21 (* Properties about atomic arity assignment on terms ************************)
  22
  23 lemma aaa_lcprs_conf: ∀L1,T,A. L1 ⊢ T ÷ A → ∀L2. L1 ⊢ ➡* L2 → L2 ⊢ T ÷ A.
  24 #L1 #T #A #HT #L2 #HL12
  25 @(TC_Conf3 … (λL,A. L ⊢ T ÷ A) … HT ? HL12) /2 width=3/
  26 qed.
  27
  28 lemma aaa_cprs_conf: ∀L,T1,A. L ⊢ T1 ÷ A → ∀T2. L ⊢ T1 ➡* T2 → L ⊢ T2 ÷ A.
  29 #L #T1 #A #HT1 #T2 #HT12
  30 @(TC_Conf3 … HT1 ? HT12) /2 width=3/
  31 qed.
  32
  33 lemma aaa_lcprs_cprs_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2. L1 ⊢ ➡* L2 →
  34                            ∀T2. L2 ⊢ T1 ➡* T2 → L2 ⊢ T2 ÷ A.
  35 /3 width=3/ qed.