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diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/llor_drop.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/llor_drop.ma
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@@ -0,0 +1,45 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2A/multiple/frees_lift.ma".
+include "basic_2A/multiple/llor_alt.ma".
+
+(* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
+
+(* Advanced properties ******************************************************)
+
+lemma llor_skip: ∀L1,L2,U,l. |L1| = |L2| → yinj (|L1|) ≤ l → L1 ⋓[U, l] L2 ≡ L1.
+#L1 #L2 #U #l #HL12 #Hl @and3_intro // -HL12
+#I1 #I2 #I #K1 #K2 #K #W1 #W2 #W #i #HLK1 #_ #HLK -L2 -K2
+lapply (drop_mono … HLK … HLK1) -HLK #H destruct
+lapply (drop_fwd_length_lt2 … HLK1) -K1
+/5 width=3 by ylt_yle_trans, ylt_inj, or3_intro0, and3_intro/
+qed.
+
+(* Note: lemma 1400 concludes the "big tree" theorem *)
+lemma llor_total: ∀L1,L2,T,l. |L1| = |L2| → ∃L. L1 ⋓[T, l] L2 ≡ L.
+#L1 @(lenv_ind_alt … L1) -L1
+[ #L2 #T #l #H >(length_inv_zero_sn … H) -L2 /2 width=2 by ex_intro/
+| #I1 #L1 #V1 #IHL1 #Y #T #l >ltail_length #H
+  elim (length_inv_pos_sn_ltail … H) -H #I2 #L2 #V2 #HL12 #H destruct
+  elim (ylt_split l (|ⓑ{I1}V1.L1|))
+  [ elim (frees_dec (ⓑ{I1}V1.L1) T l (|L1|)) #HnU
+    elim (IHL1 L2 T l) // -IHL1 -HL12
+    [ #L #HL12 >ltail_length /4 width=2 by llor_tail_frees, ylt_fwd_succ2, ex_intro/ 
+    | /4 width=2 by llor_tail_cofrees, ex_intro/
+    ]
+  | -IHL1 /4 width=2 by llor_skip, plus_minus_m_m, ex_intro/
+  ]
+]
+qed-.