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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 *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
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15 include "basic_2/unfold/tpss_tpss.ma".
16 include "basic_2/unfold/ltpss_ldrop.ma".
17 include "basic_2/static/aaa_lift.ma".
19 (* ATONIC ARITY ASSIGNMENT ON TERMS *****************************************)
21 (* Properties about parallel unfold *****************************************)
24 lemma aaa_ltpss_tpss_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 [d, e] ▶* L2 →
25 ∀T2. L2 ⊢ T1 [d, e] ▶* T2 → L2 ⊢ T2 ⁝ A.
26 #L1 #T1 #A #H elim H -L1 -T1 -A
27 [ #L1 #k #L2 #d #e #_ #T2 #H
28 >(tpss_inv_sort1 … H) -H //
29 | #I #L1 #K1 #V1 #B #i #HLK1 #_ #IHV1 #L2 #d #e #HL12 #T2 #H
30 elim (tpss_inv_lref1 … H) -H
32 elim (lt_or_ge i d) #Hdi
33 [ elim (ltpss_ldrop_conf_le … HL12 … HLK1 ?) -L1 /2 width=2/ #X #H #HLK2
34 elim (ltpss_inv_tpss11 … H ?) -H /2 width=1/ -Hdi #K2 #V2 #HK12 #HV12 #H destruct
36 | elim (lt_or_ge i (d + e)) #Hide
37 [ elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HLK2
38 elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K2 #V2 #HK12 #HV12 #H destruct
41 lapply (ltpss_ldrop_conf_ge … HL12 … HLK1 ?) -L1 // -Hide /3 width=8/
44 | * #K2 #V2 #W2 #Hdi #Hide #HLK2 #HVW2 #HWT2
45 elim (ltpss_ldrop_conf_be … HL12 … HLK1 ? ?) -L1 // /2 width=2/ #X #H #HL2K0
46 elim (ltpss_inv_tpss21 … H ?) -H /2 width=1/ -Hdi -Hide #K0 #V0 #HK12 #HV12 #H destruct
47 lapply (ldrop_mono … HL2K0 … HLK2) -HL2K0 #H destruct
48 lapply (ldrop_fwd_ldrop2 … HLK2) -HLK2 #HLK2
49 lapply (tpss_trans_eq … HV12 HVW2) -V2 /3 width=7/
51 | #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
52 elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
53 | #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
54 elim (tpss_inv_bind1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /4 width=4/
55 | #L1 #V1 #T1 #B #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
56 elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=4/
57 | #L1 #V1 #T1 #A #_ #_ #IHV1 #IHT1 #L2 #d #e #HL12 #X #H
58 elim (tpss_inv_flat1 … H) -H #V2 #T2 #HV12 #HT12 #H destruct /3 width=4/
62 lemma aaa_ltpss_tps_conf: ∀L1,T1,A. L1 ⊢ T1 ⁝ A → ∀L2,d,e. L1 [d, e] ▶* L2 →
63 ∀T2. L2 ⊢ T1 [d, e] ▶ T2 → L2 ⊢ T2 ⁝ A.
66 lemma aaa_ltpss_conf: ∀L1,T,A. L1 ⊢ T ⁝ A →
67 ∀L2,d,e. L1 [d, e] ▶* L2 → L2 ⊢ T ⁝ A.
70 lemma aaa_tpss_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
71 ∀T2,d,e. L ⊢ T1 [d, e] ▶* T2 → L ⊢ T2 ⁝ A.
74 lemma aaa_tps_conf: ∀L,T1,A. L ⊢ T1 ⁝ A →
75 ∀T2,d,e. L ⊢ T1 [d, e] ▶ T2 → L ⊢ T2 ⁝ A.