matita/matita/contribs/lambda_delta/basic_2/static/aaa_ltpss.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/unfold/ltpss.ma".
  16 include "basic_2/static/aaa_ltps.ma".
  17
  18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
  19
  20 (* Properties about parallel unfold *****************************************)
  21
  22 lemma aaa_ltpss_conf: ∀L1,T,A. L1 ⊢ T ÷ A → ∀L2,d,e. L1 [d, e] ▶* L2 → L2 ⊢ T ÷ A.
  23 #L1 #T #A #HT #L2 #d #e #HL12
  24 @(TC_Conf3 … (λL,A. L ⊢ T ÷ A) … HT ? HL12) /2 width=5/
  25 qed.
  26
  27 lemma aaa_tpss_conf: ∀L,T1,A. L ⊢ T1 ÷ A → ∀T2,d,e. L ⊢ T1 [d, e] ▶* T2 → L ⊢ T2 ÷ A.
  28 #L #T1 #A #HT1 #T2 #d #e #HT12
  29 @(TC_Conf3 … HT1 ? HT12) /2 width=5/
  30 qed.
  31
  32 lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ÷ A → ∀L2,d,e. L1 [d, e] ▶* L2 →
  33                            ∀T2. L2 ⊢ T1 [d, e] ▶* T2 → L2 ⊢ T2 ÷ A.
  34 /3 width=5/ qed.