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-(* ||A|| A project by Andrea Asperti *)
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-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
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-
-include "basic_2/substitution/drop_drop.ma".
-include "basic_2/multiple/drops.ma".
-
-(* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
-
-(* Properties concerning basic local environment slicing ********************)
-
-lemma drops_drop_trans: ∀L1,L,cs. ⬇*[Ⓕ, cs] L1 ≡ L → ∀L2,i. ⬇[i] L ≡ L2 →
- ∃∃L0,cs0,i0. ⬇[i0] L1 ≡ L0 & ⬇*[Ⓕ, cs0] L0 ≡ L2 &
- @⦃i, cs⦄ ≡ i0 & cs ▭ i ≡ cs0.
-#L1 #L #cs #H elim H -L1 -L -cs
-[ /2 width=7 by drops_nil, minuss_nil, at_nil, ex4_3_intro/
-| #L1 #L0 #L #cs #l #m #_ #HL0 #IHL0 #L2 #i #HL2
- elim (ylt_split i l) #Hil
- [ elim (drop_trans_le … HL0 … HL2) -L /2 width=2 by ylt_fwd_le/
- #L #HL0 #HL2 elim (IHL0 … HL0) -L0 /3 width=7 by drops_cons, minuss_lt, at_lt, ex4_3_intro/
- | lapply (drop_trans_ge … HL0 … HL2 ?) -L // #HL02
- elim (IHL0 … HL02) -L0 /3 width=7 by minuss_ge, at_ge, ex4_3_intro/
- ]
-]
-qed-.