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diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
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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/lrsubeqa_3.ma".
-include "basic_2/static/aaa.ma".
-
-(* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
-
-inductive lsuba (G:genv): relation lenv ≝
-| lsuba_atom: lsuba G (⋆) (⋆)
-| lsuba_bind: ∀I,L1,L2. lsuba G L1 L2 → lsuba G (L1.ⓘ{I}) (L2.ⓘ{I})
-| lsuba_beta: ∀L1,L2,W,V,A. ⦃G, L1⦄ ⊢ ⓝW.V ⁝ A → ⦃G, L2⦄ ⊢ W ⁝ A →
-              lsuba G L1 L2 → lsuba G (L1.ⓓⓝW.V) (L2.ⓛW)
-.
-
-interpretation
-  "local environment refinement (atomic arity assignment)"
-  'LRSubEqA G L1 L2 = (lsuba G L1 L2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact lsuba_inv_atom1_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → L1 = ⋆ → L2 = ⋆.
-#G #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #_ #H destruct
-| #L1 #L2 #W #V #A #_ #_ #_ #H destruct
-]
-qed-.
-
-lemma lsuba_inv_atom1: ∀G,L2. G ⊢ ⋆ ⫃⁝ L2 → L2 = ⋆.
-/2 width=4 by lsuba_inv_atom1_aux/ qed-.
-
-fact lsuba_inv_bind1_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀I,K1. L1 = K1.ⓘ{I} →
-                          (∃∃K2. G ⊢ K1 ⫃⁝ K2 & L2 = K2.ⓘ{I}) ∨
-                          ∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                      G ⊢ K1 ⫃⁝ K2 & I = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
-#G #L1 #L2 * -L1 -L2
-[ #J #K1 #H destruct
-| #I #L1 #L2 #HL12 #J #K1 #H destruct /3 width=3 by ex2_intro, or_introl/
-| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K1 #H destruct /3 width=9 by ex5_4_intro, or_intror/
-]
-qed-.
-
-lemma lsuba_inv_bind1: ∀I,G,K1,L2. G ⊢ K1.ⓘ{I} ⫃⁝ L2 →
-                       (∃∃K2. G ⊢ K1 ⫃⁝ K2 & L2 = K2.ⓘ{I}) ∨
-                       ∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A & G ⊢ K1 ⫃⁝ K2 &
-                                   I = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
-/2 width=3 by lsuba_inv_bind1_aux/ qed-.
-
-fact lsuba_inv_atom2_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → L2 = ⋆ → L1 = ⋆.
-#G #L1 #L2 * -L1 -L2
-[ //
-| #I #L1 #L2 #_ #H destruct
-| #L1 #L2 #W #V #A #_ #_ #_ #H destruct
-]
-qed-.
-
-lemma lsubc_inv_atom2: ∀G,L1. G ⊢ L1 ⫃⁝ ⋆ → L1 = ⋆.
-/2 width=4 by lsuba_inv_atom2_aux/ qed-.
-
-fact lsuba_inv_bind2_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀I,K2. L2 = K2.ⓘ{I} →
-                          (∃∃K1. G ⊢ K1 ⫃⁝ K2 & L1 = K1.ⓘ{I}) ∨
-                          ∃∃K1,V,W, A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                       G ⊢ K1 ⫃⁝ K2 & I = BPair Abst W & L1 = K1.ⓓⓝW.V.
-#G #L1 #L2 * -L1 -L2
-[ #J #K2 #H destruct
-| #I #L1 #L2 #HL12 #J #K2 #H destruct /3 width=3 by ex2_intro, or_introl/
-| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K2 #H destruct /3 width=9 by ex5_4_intro, or_intror/
-]
-qed-.
-
-lemma lsuba_inv_bind2: ∀I,G,L1,K2. G ⊢ L1 ⫃⁝ K2.ⓘ{I} →
-                       (∃∃K1. G ⊢ K1 ⫃⁝ K2 & L1 = K1.ⓘ{I}) ∨
-                       ∃∃K1,V,W,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A & G ⊢ K1 ⫃⁝ K2 &
-                                   I = BPair Abst W & L1 = K1.ⓓⓝW.V.
-/2 width=3 by lsuba_inv_bind2_aux/ qed-.
-
-(* Basic properties *********************************************************)
-
-lemma lsuba_refl: ∀G,L. G ⊢ L ⫃⁝ L.
-#G #L elim L -L /2 width=1 by lsuba_atom, lsuba_bind/
-qed.