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diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_llor.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_llor.ma
index 80bc596f2..8cbff4cd9 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_llor.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_llor.ma
@@ -18,19 +18,17 @@ include "basic_2/substitution/lleq_alt.ma".
 (* LAZY EQUIVALENCE FOR LOCAL ENVIRONMENTS **********************************)
 
 (* Properties on poinwise union for local environments **********************)
-(*
-lemma llor_lleq_O: ∀R,L1,L2,T. llpx_sn R 0 T L1 L2 →
-                   ∀L. L1 ⩖[T] L2 ≡ L → L2 ≡[T, 0] L.
-#R #L1 #L2 #T #H1 #L #H2
+
+lemma llpx_sn_llor_dx: ∀R,L1,L2.
+                       (∀U,i. L2 ⊢ i ϵ 𝐅*[0]⦃U⦄ → L1 ⊢ i ϵ 𝐅*[0]⦃U⦄) →
+                       ∀T. llpx_sn R 0 T L1 L2 → ∀L. L1 ⩖[T] L2 ≡ L → L2 ≡[T, 0] L.
+#R #L1 #L2 #HR #T #H1 #L #H2
 elim (llpx_sn_llpx_sn_alt … H1) -H1 #HL12 #IH1
 elim H2 -H2 #_ #HL1 #IH2
 @lleq_intro_alt // #I2 #I #K2 #K #V2 #V #i #Hi #HnT #HLK2 #HLK
 lapply (ldrop_fwd_length_lt2 … HLK) #HiL
 elim (ldrop_O1_lt (Ⓕ) L1 i) // -HiL #I1 #K1 #V1 #HLK1
-elim (IH1 … HLK1 HLK2) // -IH1
-[ #H #_ destruct
-  elim (IH2 … HLK1 HLK2 HLK) * /2 width=1 by conj/
-  #H elim HnT -HnT
-| #H @HnT -HnT
-]
-*)
+elim (IH1 … HLK1 HLK2) -IH1 /2 width=1 by/ #H #_ destruct
+elim (IH2 … HLK1 HLK2 HLK) -IH2 -HLK1 -HLK2 -HLK * /2 width=1 by conj/ #H
+elim H -H /2 width=1 by/
+qed.