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15 include "Basic_2/substitution/ldrop.ma".
16 include "Basic_2/unfold/lifts.ma".
18 (* GENERIC LOCAL ENVIRONMENT SLICING ****************************************)
20 inductive ldrops: list2 nat nat → relation lenv ≝
21 | ldrops_nil : ∀L. ldrops ⟠ L L
22 | ldrops_cons: ∀L1,L,L2,des,d,e.
23 ldrops des L1 L → ⇩[d,e] L ≡ L2 → ldrops ({d, e} :: des) L1 L2
26 interpretation "generic local environment slicing"
27 'RDropStar des T1 T2 = (ldrops des T1 T2).
29 (* Basic properties *********************************************************)
31 lemma ldrops_skip: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 → ∀V1,V2. ⇧*[des] V2 ≡ V1 →
32 ∀I. ⇩*[ss des] L1. 𝕓{I} V1 ≡ L2. 𝕓{I} V2.
33 #L1 #L2 #des #H elim H -L1 -L2 -des
35 >(lifts_inv_nil … HV12) -HV12 //
36 | #L1 #L #L2 #des #d #e #_ #HL2 #IHL #V1 #V2 #H #I
37 elim (lifts_inv_cons … H) -H /3 width=5/