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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/reducibility/lcpr_aaa.ma".
16 include "basic_2/computation/cprs.ma".
17 include "basic_2/computation/lcprs.ma".
19 (* CONTEXT-SENSITIVE PARALLEL COMPUTATION ON LOCAL ENVIRONMENTS *************)
21 (* Properties about atomic arity assignment on terms ************************)
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/
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/
33 lemma aaa_lcprs_cprs_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2. L1 ⊢ ➡* L2 →
34 ∀T2. L2 ⊢ T1 ➡* T2 → L2 ⊢ T2 ⁝ A.