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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/relocation/ldrop_ldrop.ma".
16 include "basic_2/static/da.ma".
18 (* DEGREE ASSIGNMENT FOR TERMS **********************************************)
20 (* Properties on relocation *************************************************)
22 lemma da_lift: ∀h,g,G,L1,T1,l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l →
23 ∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
24 ⦃G, L2⦄ ⊢ T2 ▪[h, g] l.
25 #h #g #G #L1 #T1 #l #H elim H -G -L1 -T1 -l
26 [ #G #L1 #k #l #Hkl #L2 #d #e #_ #X #H
27 >(lift_inv_sort1 … H) -X /2 width=1/
28 | #G #L1 #K1 #V1 #i #l #HLK1 #_ #IHV1 #L2 #d #e #HL21 #X #H
29 elim (lift_inv_lref1 … H) * #Hid #H destruct
30 [ elim (ldrop_trans_le … HL21 … HLK1) -L1 /2 width=2/ #X #HLK2 #H
31 elim (ldrop_inv_skip2 … H) -H /2 width=1/ -Hid #K2 #V2 #HK21 #HV12 #H destruct
33 | lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 // -Hid /3 width=7/
35 | #G #L1 #K1 #W1 #i #l #HLK1 #_ #IHW1 #L2 #d #e #HL21 #X #H
36 elim (lift_inv_lref1 … H) * #Hid #H destruct
37 [ elim (ldrop_trans_le … HL21 … HLK1) -L1 /2 width=2/ #X #HLK2 #H
38 elim (ldrop_inv_skip2 … H) -H /2 width=1/ -Hid #K2 #W2 #HK21 #HW12 #H destruct
40 | lapply (ldrop_trans_ge … HL21 … HLK1 ?) -L1 // -Hid /3 width=7/
42 | #a #I #G #L1 #V1 #T1 #l #_ #IHT1 #L2 #d #e #HL21 #X #H
43 elim (lift_inv_bind1 … H) -H #V2 #T2 #HV12 #HU12 #H destruct /4 width=4/
44 | #I #G #L1 #V1 #T1 #l #_ #IHT1 #L2 #d #e #HL21 #X #H
45 elim (lift_inv_flat1 … H) -H #V2 #T2 #HV12 #HU12 #H destruct /3 width=4/
49 (* Inversion lemmas on relocation *******************************************)
51 lemma da_inv_lift: ∀h,g,G,L2,T2,l. ⦃G, L2⦄ ⊢ T2 ▪[h, g] l →
52 ∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
53 ⦃G, L1⦄ ⊢ T1 ▪[h, g] l.
54 #h #g #G #L2 #T2 #l #H elim H -G -L2 -T2 -l
55 [ #G #L2 #k #l #Hkl #L1 #d #e #_ #X #H
56 >(lift_inv_sort2 … H) -X /2 width=1/
57 | #G #L2 #K2 #V2 #i #l #HLK2 #HV2 #IHV2 #L1 #d #e #HL21 #X #H
58 elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HV2 | -IHV2 ]
59 [ elim (ldrop_conf_lt … HL21 … HLK2) -L2 // /3 width=7/
60 | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 // /2 width=4/
62 | #G #L2 #K2 #W2 #i #l #HLK2 #HW2 #IHW2 #L1 #d #e #HL21 #X #H
63 elim (lift_inv_lref2 … H) * #Hid #H destruct [ -HW2 | -IHW2 ]
64 [ elim (ldrop_conf_lt … HL21 … HLK2) -L2 // /3 width=7/
65 | lapply (ldrop_conf_ge … HL21 … HLK2 ?) -L2 // /2 width=4/
67 | #a #I #G #L2 #V2 #T2 #l #_ #IHT2 #L1 #d #e #HL21 #X #H
68 elim (lift_inv_bind2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /4 width=4/
69 | #I #G #L2 #V2 #T2 #l #_ #IHT2 #L1 #d #e #HL21 #X #H
70 elim (lift_inv_flat2 … H) -H #V1 #T1 #HV12 #HT12 #H destruct /3 width=4/