inductive ldrops: list2 nat nat → relation lenv ≝
| ldrops_nil : ∀L. ldrops ⟠ L L
| ldrops_cons: ∀L1,L,L2,des,d,e.
- ldrops des L1 L â\86\92 â\87\93[d,e] L ≡ L2 → ldrops ({d, e} :: des) L1 L2
+ ldrops des L1 L â\86\92 â\87©[d,e] L ≡ L2 → ldrops ({d, e} :: des) L1 L2
.
interpretation "generic local environment slicing"
- 'RLDrop des T1 T2 = (ldrops des T1 T2).
+ 'RDropStar des T1 T2 = (ldrops des T1 T2).
(* Basic properties *********************************************************)
-lemma ldrops_skip: â\88\80L1,L2,des. â\87\93[des] L1 â\89¡ L2 â\86\92 â\88\80V1,V2. â\87\91[des] V2 ≡ V1 →
- â\88\80I. â\87\93[ss des] L1. 𝕓{I} V1 ≡ L2. 𝕓{I} V2.
+lemma ldrops_skip: â\88\80L1,L2,des. â\87©*[des] L1 â\89¡ L2 â\86\92 â\88\80V1,V2. â\87§*[des] V2 ≡ V1 →
+ â\88\80I. â\87©*[des + 1] L1. 𝕓{I} V1 ≡ L2. 𝕓{I} V2.
#L1 #L2 #des #H elim H -L1 -L2 -des
[ #L #V1 #V2 #HV12 #I
>(lifts_inv_nil … HV12) -HV12 //
elim (lifts_inv_cons … H) -H /3 width=5/
].
qed.
+
+(* Basic_1: removed theorems 1: drop1_getl_trans
+*)
+(*
+lemma ldrops_inv_skip2: ∀des2,L1,I,K2,V2. ⇩*[des2] L1 ≡ K2. 𝕓{I} V2 →
+ ∀des,i. des ▭ i ≡ des2 →
+ ∃∃K1,V1,des1. des ▭ (i + 1) ≡ des1 &
+ ⇩*[des1] K1 ≡ K2 &
+ ⇧*[des1] V2 ≡ V1 &
+ L1 = K1. 𝕓{I} V1.
+*)
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