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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_2A/static/aaa_aaa.ma".
16 include "basic_2A/static/lsuba.ma".
18 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
20 (* Properties concerning atomic arity assignment ****************************)
22 lemma lsuba_aaa_conf: ∀G,L1,V,A. ⦃G, L1⦄ ⊢ V ⁝ A →
23 ∀L2. G ⊢ L1 ⫃⁝ L2 → ⦃G, L2⦄ ⊢ V ⁝ A.
24 #G #L1 #V #A #H elim H -G -L1 -V -A
26 | #I #G #L1 #K1 #V #A #i #HLK1 #HV #IHV #L2 #HL12
27 elim (lsuba_drop_O1_conf … HL12 … HLK1) -L1 #X #H #HLK2
28 elim (lsuba_inv_pair1 … H) -H * #K2
29 [ #HK12 #H destruct /3 width=5 by aaa_lref/
30 | #W0 #V0 #A0 #HV0 #HW0 #_ #H1 #H2 #H3 destruct
31 lapply (aaa_mono … HV0 … HV) #H destruct -V0 /2 width=5 by aaa_lref/
33 | /4 width=2 by lsuba_pair, aaa_abbr/
34 | /4 width=1 by lsuba_pair, aaa_abst/
35 | /3 width=3 by aaa_appl/
36 | /3 width=1 by aaa_cast/
40 lemma lsuba_aaa_trans: ∀G,L2,V,A. ⦃G, L2⦄ ⊢ V ⁝ A →
41 ∀L1. G ⊢ L1 ⫃⁝ L2 → ⦃G, L1⦄ ⊢ V ⁝ A.
42 #G #L2 #V #A #H elim H -G -L2 -V -A
44 | #I #G #L2 #K2 #V #A #i #HLK2 #H1V #IHV #L1 #HL12
45 elim (lsuba_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
46 elim (lsuba_inv_pair2 … H) -H * #K1
47 [ #HK12 #H destruct /3 width=5 by aaa_lref/
48 | #V0 #A0 #HV0 #H2V #_ #H1 #H2 destruct
49 lapply (aaa_mono … H2V … H1V) #H destruct -K2 /2 width=5 by aaa_lref/
51 | /4 width=2 by lsuba_pair, aaa_abbr/
52 | /4 width=1 by lsuba_pair, aaa_abst/
53 | /3 width=3 by aaa_appl/
54 | /3 width=1 by aaa_cast/