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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/dynamic/lsubn.ma".
17 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE TYPE ASSIGNMENT ******************)
19 (* Properties concerning basic local environment slicing ********************)
21 (* Note: the constant 0 cannot be generalized *)
22 lemma lsubn_ldrop_O1_conf: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀K1,e. ⇩[0, e] L1 ≡ K1 →
23 ∃∃K2. h ⊢ K1 :⊑ K2 & ⇩[0, e] L2 ≡ K2.
24 #h #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 #H1VW #H2VW #_ #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 (* Basic_1: was only: csubt_drop_abbr csubt_drop_abst *)
45 lemma lsubn_ldrop_O1_trans: ∀h,L1,L2. h ⊢ L1 :⊑ L2 → ∀K2,e. ⇩[0, e] L2 ≡ K2 →
46 ∃∃K1. h ⊢ K1 :⊑ K2 & ⇩[0, e] L1 ≡ K1.
47 #h #L1 #L2 #H elim H -L1 -L2
49 | #I #L1 #L2 #V #_ #IHL12 #K2 #e #H
50 elim (ldrop_inv_O1 … H) -H * #He #HLK2
52 elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
53 <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
54 | elim (IHL12 … HLK2) -L2 /3 width=3/
56 | #L1 #L2 #V #W #H1VW #H2VW #_ #IHL12 #K2 #e #H
57 elim (ldrop_inv_O1 … H) -H * #He #HLK2
59 elim (IHL12 L2 0 ?) -IHL12 // #X #HL12 #H
60 <(ldrop_inv_refl … H) in HL12; -H /3 width=3/
61 | elim (IHL12 … HLK2) -L2 /3 width=3/