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diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma
index b96a2ddcc..a1ca60e4c 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma
@@ -33,8 +33,9 @@ lemma lreq_drops_trans_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
                              ∀b,f,I,K2. ⬇*[b, f] L2 ≡ K2.ⓘ{I} → 𝐔⦃f⦄ →
                              ∀f1. f ~⊚ ⫯f1 ≡ f2 →
                              ∃∃K1. ⬇*[b, f] L1 ≡ K1.ⓘ{I} & K1 ≡[f1] K2.
-#f2 #L1 #L2 #HL12 #b #f #I #K1 #HLK1 #Hf #f1 #Hf2
-elim (lexs_drops_trans_next … HL12 … HLK1 Hf … Hf2) -f2 -L2 -Hf
+#f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
+elim (lexs_drops_trans_next … HL12 … HLK2 Hf … Hf2) -f2 -L2 -Hf
+#I1 #K1 #HLK1 #HK12 #H <(ceq_ext_inv_eq … H) -I2
 /2 width=3 by ex2_intro/
 qed-.
 
@@ -43,7 +44,7 @@ lemma lreq_drops_conf_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
                             ∀b,f,I,K1. ⬇*[b, f] L1 ≡ K1.ⓘ{I} → 𝐔⦃f⦄ →
                             ∀f1. f ~⊚ ⫯f1 ≡ f2 →
                             ∃∃K2. ⬇*[b, f] L2 ≡ K2.ⓘ{I} & K1 ≡[f1] K2.
-#f2 #L1 #L2 #HL12 #b #f #I #K1 #HLK1 #Hf #f1 #Hf2
+#f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
 elim (lreq_drops_trans_next … (lreq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
 /3 width=3 by lreq_sym, ex2_intro/
 qed-.
@@ -52,6 +53,9 @@ lemma drops_lreq_trans_next: ∀f1,K1,K2. K1 ≡[f1] K2 →
                              ∀b,f,I,L1. ⬇*[b, f] L1.ⓘ{I} ≡ K1 →
                              ∀f2. f ~⊚ f1 ≡ ⫯f2 →
                              ∃∃L2. ⬇*[b, f] L2.ⓘ{I} ≡ K2 & L1 ≡[f2] L2 & L1.ⓘ{I} ≡[f] L2.ⓘ{I}.
-#f1 #K1 #K2 #HK12 #b #f #I #L1 #HLK1 #f2 #Hf2
+#f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
 elim (drops_lexs_trans_next … HK12 … HLK1 … Hf2) -f1 -K1
-/2 width=6 by cfull_lift_sn, ceq_lift_sn, ex3_intro/ qed-.
+/2 width=6 by cfull_lift_sn, ceq_lift_sn/
+#I2 #L2 #HLK2 #HL12 #H >(ceq_ext_inv_eq … H) -I1
+/2 width=4 by ex3_intro/
+qed-.