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diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_new/lleq/lleq_alt.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_new/lleq/lleq_alt.etc
deleted file mode 100644
index d2919f5b6..000000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_new/lleq/lleq_alt.etc
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@@ -1,41 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/multiple/llpx_sn_alt.ma".
-include "basic_2/multiple/lleq.ma".
-
-(* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
-
-(* Alternative definition (not recursive) ***********************************)
-
-theorem lleq_intro_alt: ∀L1,L2,T,l. |L1| = |L2| →
-                        (∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ →
-                           ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 →
-                           I1 = I2 ∧ V1 = V2
-                        ) → L1 ≡[T, l] L2.
-#L1 #L2 #T #l #HL12 #IH @llpx_sn_alt_inv_llpx_sn @conj // -HL12
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hil #HnT #HLK1 #HLK2
-@(IH … HnT HLK1 HLK2) -IH -HnT -HLK1 -HLK2 //
-qed.
-
-theorem lleq_inv_alt: ∀L1,L2,T,l. L1 ≡[T, l] L2 →
-                      |L1| = |L2| ∧
-                      ∀I1,I2,K1,K2,V1,V2,i. l ≤ yinj i → L1 ⊢ i ϵ 𝐅*[l]⦃T⦄ →
-                      ⬇[i] L1 ≡ K1.ⓑ{I1}V1 → ⬇[i] L2 ≡ K2.ⓑ{I2}V2 →
-                      I1 = I2 ∧ V1 = V2.
-#L1 #L2 #T #l #H elim (llpx_sn_llpx_sn_alt … H) -H
-#HL12 #IH @conj //
-#I1 #I2 #K1 #K2 #V1 #V2 #i #Hil #HnT #HLK1 #HLK2
-@(IH … HnT HLK1 HLK2) -IH -HnT -HLK1 -HLK2 //
-qed-.