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diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma
index ca8035680..2a8873d9b 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma
@@ -85,12 +85,20 @@ lemma lleq_inv_lref_ge_sn: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 → d ≤ i →
 /3 width=4 by lleq_sym, ex2_2_intro/
 qed-.
 
-lemma lleq_inv_lref_ge: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 → d ≤ i →
-                        ∀I1,I2,K1,K2,V.
-                        ⇩[i] L1 ≡ K1.ⓑ{I1}V → ⇩[i] L2 ≡ K2.ⓑ{I2}V → K1 ⋕[V, 0] K2.
-#L1 #L2 #d #i #HL12 #Hdi #I1 #I2 #K1 #K2 #V #HLK1 #HLK2
+lemma lleq_inv_lref_ge_gen: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 → d ≤ i →
+                            ∀I1,I2,K1,K2,V1,V2.
+                            ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 →
+                            V1 = V2 ∧ K1 ⋕[V2, 0] K2.
+#L1 #L2 #d #i #HL12 #Hdi #I1 #I2 #K1 #K2 #V1 #V2 #HLK1 #HLK2
 elim (lleq_inv_lref_ge_sn … HL12 … HLK1) // -L1 -d
-#J #Y #HY lapply (ldrop_mono … HY … HLK2) -L2 -i #H destruct //
+#J #Y #HY lapply (ldrop_mono … HY … HLK2) -L2 -i #H destruct /2 width=1 by conj/
+qed-.
+
+lemma lleq_inv_lref_ge: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 → d ≤ i →
+                        ∀I,K1,K2,V. ⇩[i] L1 ≡ K1.ⓑ{I}V → ⇩[i] L2 ≡ K2.ⓑ{I}V →
+                        K1 ⋕[V, 0] K2.
+#L1 #L2 #d #i #HL12 #Hdi #I #K1 #K2 #V #HLK1 #HLK2
+elim (lleq_inv_lref_ge_gen … HL12 … HLK1 HLK2) //
 qed-.
 
 (* Advanced properties ******************************************************)