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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/reduction/crx.ma".
18 (* CONTEXT-SENSITIVE EXTENDED REDUCIBLE TERMS *******************************)
20 (* Properties on relocation *************************************************)
22 lemma crx_lift: ∀h,g,G,K,T. ⦃G, K⦄ ⊢ 𝐑[h, g]⦃T⦄ → ∀L,d,e. ⇩[d, e] L ≡ K →
23 ∀U. ⇧[d, e] T ≡ U → ⦃G, L⦄ ⊢ 𝐑[h, g]⦃U⦄.
24 #h #g #G #K #T #H elim H -K -T
25 [ #K #k #l #Hkl #L #d #e #_ #X #H
26 >(lift_inv_sort1 … H) -X /2 width=2/
27 | #I #K #K0 #V #i #HK0 #L #d #e #HLK #X #H
28 elim (lift_inv_lref1 … H) -H * #Hid #H destruct
29 [ elim (ldrop_trans_lt … HLK … HK0) -K // /2 width=4/
30 | lapply (ldrop_trans_ge … HLK … HK0 ?) -K // /2 width=4/
32 | #K #V #T #_ #IHV #L #d #e #HLK #X #H
33 elim (lift_inv_flat1 … H) -H #W #U #HVW #_ #H destruct /3 width=4/
34 | #K #V #T #_ #IHT #L #d #e #HLK #X #H
35 elim (lift_inv_flat1 … H) -H #W #U #_ #HTU #H destruct /3 width=4/
36 | #I #K #V #T #HI #L #d #e #_ #X #H
37 elim (lift_fwd_pair1 … H) -H #W #U #_ #H destruct /2 width=1/
38 | #a #I #K #V #T #HI #_ #IHV #L #d #e #HLK #X #H
39 elim (lift_inv_bind1 … H) -H #W #U #HVW #_ #H destruct /3 width=4/
40 | #a #I #K #V #T #HI #_ #IHT #L #d #e #HLK #X #H
41 elim (lift_inv_bind1 … H) -H #W #U #HVW #HTU #H destruct /4 width=4/
42 | #a #K #V #V0 #T #L #d #e #_ #X #H
43 elim (lift_inv_flat1 … H) -H #W #X0 #_ #H0 #H destruct
44 elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1/
45 | #a #K #V #V0 #T #L #d #e #_ #X #H
46 elim (lift_inv_flat1 … H) -H #W #X0 #_ #H0 #H destruct
47 elim (lift_inv_bind1 … H0) -H0 #W0 #U #_ #_ #H0 destruct /2 width=1/
51 lemma crx_inv_lift: ∀h,g,G,L,U. ⦃G, L⦄ ⊢ 𝐑[h, g]⦃U⦄ → ∀K,d,e. ⇩[d, e] L ≡ K →
52 ∀T. ⇧[d, e] T ≡ U → ⦃G, K⦄ ⊢ 𝐑[h, g]⦃T⦄.
53 #h #g #G #L #U #H elim H -L -U
54 [ #L #k #l #Hkl #K #d #e #_ #X #H
55 >(lift_inv_sort2 … H) -X /2 width=2/
56 | #I #L #L0 #W #i #HK0 #K #d #e #HLK #X #H
57 elim (lift_inv_lref2 … H) -H * #Hid #H destruct
58 [ elim (ldrop_conf_lt … HLK … HK0) -L // /2 width=4/
59 | lapply (ldrop_conf_ge … HLK … HK0 ?) -L // /2 width=4/
61 | #L #W #U #_ #IHW #K #d #e #HLK #X #H
62 elim (lift_inv_flat2 … H) -H #V #T #HVW #_ #H destruct /3 width=4/
63 | #L #W #U #_ #IHU #K #d #e #HLK #X #H
64 elim (lift_inv_flat2 … H) -H #V #T #_ #HTU #H destruct /3 width=4/
65 | #I #L #W #U #HI #K #d #e #_ #X #H
66 elim (lift_fwd_pair2 … H) -H #V #T #_ #H destruct /2 width=1/
67 | #a #I #L #W #U #HI #_ #IHW #K #d #e #HLK #X #H
68 elim (lift_inv_bind2 … H) -H #V #T #HVW #_ #H destruct /3 width=4/
69 | #a #I #L #W #U #HI #_ #IHU #K #d #e #HLK #X #H
70 elim (lift_inv_bind2 … H) -H #V #T #HVW #HTU #H destruct /4 width=4/
71 | #a #L #W #W0 #U #K #d #e #_ #X #H
72 elim (lift_inv_flat2 … H) -H #V #X0 #_ #H0 #H destruct
73 elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1/
74 | #a #L #W #W0 #U #K #d #e #_ #X #H
75 elim (lift_inv_flat2 … H) -H #V #X0 #_ #H0 #H destruct
76 elim (lift_inv_bind2 … H0) -H0 #V0 #T #_ #_ #H0 destruct /2 width=1/