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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/reducibility/ltpr_aaa.ma".
16 include "basic_2/reducibility/cpr.ma".
17 include "basic_2/reducibility/lcpr.ma".
19 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *************)
21 (* Properties about atomic arity assignment on terms ************************)
23 lemma aaa_lcpr_conf: ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L2. L1 ⊢ ➡ L2 → L2 ⊢ T ⁝ A.
24 #L1 #T #A #HT #L2 * /3 width=5/
27 lemma aaa_cpr_conf: ∀L,T1,A. L ⊢ T1 ⁝ A → ∀T2. L ⊢ T1 ➡ T2 → L ⊢ T2 ⁝ A.
28 #L #T1 #A #HT1 #T2 * /3 width=5/
31 lemma aaa_lcpr_cpr_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2. L1 ⊢ ➡ L2 →
32 ∀T2. L2 ⊢ T1 ➡ T2 → L2 ⊢ T2 ⁝ A.