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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/llor/llor.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/llor/llor.etc
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--- a/matita/matita/contribs/lambdadelta/basic_2/etc/llor/llor.etc
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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_2/notation/relations/lazyor_4.ma".
-include "basic_2/relocation/lpx_sn.ma".
-include "basic_2/substitution/cofrees.ma".
-
-(* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
-
-inductive clor (T) (L2) (K1) (V1): predicate term ≝
-| clor_sn: |K1| < |L2| → K1 ⊢ |L2|-|K1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ → clor T L2 K1 V1 V1
-| clor_dx: ∀I,K2,V2. |K1| < |L2| → (K1 ⊢ |L2|-|K1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) →
-           ⇩[|L2|-|K1|-1] L2 ≡ K2.ⓑ{I}V2 → clor T L2 K1 V1 V2
-.
-
-definition llor: relation4 term lenv lenv lenv ≝
-                 λT,L2. lpx_sn (clor T L2).
-
-interpretation
-   "lazy union (local environment)"
-   'LazyOr L1 T L2 L = (llor T L2 L1 L).
-
-(* Basic properties *********************************************************)
-
-lemma llor_pair_sn: ∀I,L1,L2,L,V,T. L1 ⩖[T] L2 ≡ L →
-                    |L1| < |L2| → L1 ⊢ |L2|-|L1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ →
-                    L1.ⓑ{I}V ⩖[T] L2 ≡ L.ⓑ{I}V.
-/3 width=2 by clor_sn, lpx_sn_pair/ qed.
-
-lemma llor_pair_dx: ∀I,J,L1,L2,L,K2,V1,V2,T. L1 ⩖[T] L2 ≡ L →
-                    |L1| < |L2| → (L1 ⊢ |L2|-|L1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) →
-                    ⇩[|L2|-|L1|-1] L2 ≡ K2.ⓑ{J}V2 →
-                    L1.ⓑ{I}V1 ⩖[T] L2 ≡ L.ⓑ{I}V2.
-/4 width=3 by clor_dx, lpx_sn_pair/ qed.
-
-lemma llor_total: ∀T,L2,L1. |L1| ≤ |L2| → ∃L. L1 ⩖[T] L2 ≡ L.
-#T #L2 #L1 elim L1 -L1 /2 width=2 by ex_intro/
-#L1 #I1 #V1 #IHL1 normalize
-#H elim IHL1 -IHL1 /2 width=3 by transitive_le/
-#L #HT elim (cofrees_dec L1 T 0 (|L2|-|L1|-1))
-[ /3 width=2 by llor_pair_sn, ex_intro/
-| elim (ldrop_O1_lt (Ⓕ) L2 (|L2|-|L1|-1))
-  /5 width=4 by llor_pair_dx, monotonic_lt_minus_l, ex_intro/
-]
-qed-.