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14
15 include "basic_2/unfold/ltpss_sn_alt.ma".
16 include "basic_2/static/aaa_ltpss_dx.ma".
17
18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
19
20 (* Properties about sn parallel unfold **************************************)
21
22 lemma aaa_ltpss_sn_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
23                          ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 → L2 ⊢ T ⁝ A.
24 #L1 #T #A #HT #L2 #d #e #HL12
25 lapply (ltpss_sn_ltpssa … HL12) -HL12 #HL12
26 @(TC_Conf3 … (λL,A. L ⊢ T ⁝ A) … HT ? HL12) /2 width=5/
27 qed.
28
29 lemma aaa_ltpss_sn_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
30                               ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
31                               ∀T2. L2 ⊢ T1 ▶* [d, e] T2 → L2 ⊢ T2 ⁝ A.
32 /3 width=5/ qed.
33
34 lemma aaa_ltpss_sn_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A →
35                              ∀L2,d,e. L1 ⊢ ▶* [d, e] L2 →
36                              ∀T2. L2 ⊢ T1 ▶ [d, e] T2 → L2 ⊢ T2 ⁝ A.
37 /3 width=5/ qed.