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14
15 include "basic_2/static/aaa_ltpss_sn.ma".
16 include "basic_2/reducibility/ltpr_aaa.ma".
17 include "basic_2/reducibility/cpr.ma".
18 include "basic_2/reducibility/lcpr.ma".
19
20 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS *************)
21
22 (* Properties about atomic arity assignment on terms ************************)
23
24 lemma aaa_lcpr_conf: ∀L1,T,A. L1 ⊢ T ⁝ A → ∀L2. L1 ⊢ ➡ L2 → L2 ⊢ T ⁝ A.
25 #L1 #T #A #HT #L2 * /3 width=5/
26 qed.
27
28 lemma aaa_cpr_conf: ∀L,T1,A. L ⊢ T1 ⁝ A → ∀T2. L ⊢ T1 ➡ T2 → L ⊢ T2 ⁝ A.
29 #L #T1 #A #HT1 #T2 * /3 width=5/
30 qed.
31
32 lemma aaa_lcpr_cpr_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2. L1 ⊢ ➡ L2 →
33                          ∀T2. L2 ⊢ T1 ➡ T2 → L2 ⊢ T2 ⁝ A.
34 /3 width=3/ qed.