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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_2/static/lsuba.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
19 (* Properties concerning basic local environment slicing ********************)
21 (* Note: the constant 0 cannot be generalized *)
22 lemma lsuba_ldrop_O1_conf: ∀L1,L2. L1 ⁝⊑ L2 → ∀K1,e. ⇩[0, e] L1 ≡ K1 →
23 ∃∃K2. K1 ⁝⊑ K2 & ⇩[0, e] L2 ≡ K2.
24 #L1 #L2 #H elim H -L1 -L2
26 | #I #L1 #L2 #V #_ #IHL12 #K1 #e #H
27 elim (ldrop_inv_O1 … H) -H * #He #HLK1
29 elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
30 <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
31 | elim (IHL12 … HLK1) -L1 /3 width=3/
33 | #L1 #L2 #V #W #A #HV #HW #_ #IHL12 #K1 #e #H
34 elim (ldrop_inv_O1 … H) -H * #He #HLK1
36 elim (IHL12 L1 0 ?) -IHL12 // #X #HL12 #H
37 <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
38 | elim (IHL12 … HLK1) -L1 /3 width=3/
43 (* Note: the constant 0 cannot be generalized *)
44 lemma lsuba_ldrop_O1_trans: ∀L1,L2. L1 ⁝⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
45 ∃∃K1. K1 ⁝⊑ K2 & ⇩[0, e] L1 ≡ K1.
46 #L1 #L2 #H elim H -L1 -L2
48 | #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
49 elim (ldrop_inv_O1 … H) -H * #He #HLK2
51 elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
52 <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
53 | elim (IHL12 … HLK2) -L2 /3 width=3/
55 | #L1 #L2 #V #W #A #HV #HW #_ #IHL12 #K2 #e #H
56 elim (ldrop_inv_O1 … H) -H * #He #HLK2
58 elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
59 <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
60 | elim (IHL12 … HLK2) -L2 /3 width=3/