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14
15 include "basic_2A/multiple/lleq_drop.ma".
16 include "basic_2A/static/aaa.ma".
17
18 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
19
20 (* Properties on lazy equivalence for local environments ********************)
21
22 lemma lleq_aaa_trans: ∀G,L2,T,A. ⦃G, L2⦄ ⊢ T ⁝ A →
23                       ∀L1. L1 ≡[T, 0] L2 → ⦃G, L1⦄ ⊢ T ⁝ A.
24 #G #L2 #T #A #H elim H -G -L2 -T -A /2 width=1 by aaa_sort/
25 [ #I #G #L2 #K2 #V2 #A #i #HLK2 #_ #IHV2 #L1 #H elim (lleq_fwd_lref_dx … H … HLK2) -L2
26   [ #H elim (ylt_yle_false … H) //
27   | * /3 width=5 by aaa_lref/
28   ]
29 | #a #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H elim (lleq_inv_bind_O … H) -H
30   /3 width=2 by aaa_abbr/
31 | #a #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H elim (lleq_inv_bind_O … H) -H
32   /3 width=1 by aaa_abst/
33 | #G #L2 #V #T #B #A #_ #_ #IHV #IHT #L1 #H elim (lleq_inv_flat … H) -H
34   /3 width=3 by aaa_appl/
35 | #G #L2 #V #T #A #_ #_ #IHV #IHT #L1 #H elim (lleq_inv_flat … H) -H
36   /3 width=1 by aaa_cast/
37 ]
38 qed-.
39
40 lemma aaa_lleq_conf: ∀G,L2,T,A. ⦃G, L2⦄ ⊢ T ⁝ A →
41                      ∀L1. L2 ≡[T, 0] L1 → ⦃G, L1⦄ ⊢ T ⁝ A.
42 /3 width=3 by lleq_aaa_trans, lleq_sym/ qed-.