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diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma
index dfee0330d..18519b6fc 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lexs.ma
@@ -118,7 +118,7 @@ lemma lexs_co_dropable_dx: ∀RN,RP. co_dropable_dx (lexs RN RP).
 lemma lexs_drops_conf_next: ∀RN,RP.
                             ∀f2,L1,L2. L1 ⪤*[RN, RP, f2] L2 →
                             ∀b,f,I1,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I1} → 𝐔⦃f⦄ →
-                            ∀f1. f ~⊚ ⫯f1 ≘ f2 →
+                            ∀f1. f ~⊚ ↑f1 ≘ f2 →
                             ∃∃I2,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I2} & K1 ⪤*[RN, RP, f1] K2 & RN K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
 elim (lexs_co_dropable_sn … HLK1 … Hf … HL12 … Hf2) -L1 -f2 -Hf
@@ -129,7 +129,7 @@ qed-.
 lemma lexs_drops_conf_push: ∀RN,RP.
                             ∀f2,L1,L2. L1 ⪤*[RN, RP, f2] L2 →
                             ∀b,f,I1,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I1} → 𝐔⦃f⦄ →
-                            ∀f1. f ~⊚ ↑f1 ≘ f2 →
+                            ∀f1. f ~⊚ ⫯f1 ≘ f2 →
                             ∃∃I2,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I2} & K1 ⪤*[RN, RP, f1] K2 & RP K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
 elim (lexs_co_dropable_sn … HLK1 … Hf … HL12 … Hf2) -L1 -f2 -Hf
@@ -140,7 +140,7 @@ qed-.
 (* Basic_2A1: includes: lpx_sn_drop_trans *)
 lemma lexs_drops_trans_next: ∀RN,RP,f2,L1,L2. L1 ⪤*[RN, RP, f2] L2 →
                              ∀b,f,I2,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I2} → 𝐔⦃f⦄ →
-                             ∀f1. f ~⊚ ⫯f1 ≘ f2 →
+                             ∀f1. f ~⊚ ↑f1 ≘ f2 →
                              ∃∃I1,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I1} & K1 ⪤*[RN, RP, f1] K2 & RN K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
 elim (lexs_co_dropable_dx … HL12 … HLK2 … Hf … Hf2) -L2 -f2 -Hf
@@ -150,7 +150,7 @@ qed-.
 
 lemma lexs_drops_trans_push: ∀RN,RP,f2,L1,L2. L1 ⪤*[RN, RP, f2] L2 →
                              ∀b,f,I2,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I2} → 𝐔⦃f⦄ →
-                             ∀f1. f ~⊚ ↑f1 ≘ f2 →
+                             ∀f1. f ~⊚ ⫯f1 ≘ f2 →
                              ∃∃I1,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I1} & K1 ⪤*[RN, RP, f1] K2 & RP K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
 elim (lexs_co_dropable_dx … HL12 … HLK2 … Hf … Hf2) -L2 -f2 -Hf
@@ -162,7 +162,7 @@ lemma drops_lexs_trans_next: ∀RN,RP. (∀L. reflexive ? (RN L)) → (∀L. ref
                              d_liftable2_sn … liftsb RN → d_liftable2_sn … liftsb RP →
                              ∀f1,K1,K2. K1 ⪤*[RN, RP, f1] K2 →
                              ∀b,f,I1,L1. ⬇*[b, f] L1.ⓘ{I1} ≘ K1 →
-                             ∀f2. f ~⊚ f1 ≘ ⫯f2 →
+                             ∀f2. f ~⊚ f1 ≘ ↑f2 →
                              ∃∃I2,L2. ⬇*[b, f] L2.ⓘ{I2} ≘ K2 & L1 ⪤*[RN, RP, f2] L2 & RN L1 I1 I2 & L1.ⓘ{I1} ≡[f] L2.ⓘ{I2}.
 #RN #RP #H1RN #H1RP #H2RN #H2RP #f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
 elim (lexs_liftable_co_dedropable_sn … H1RN H1RP H2RN H2RP … HLK1 … HK12 … Hf2) -K1 -f1 -H1RN -H1RP -H2RN -H2RP
@@ -174,7 +174,7 @@ lemma drops_lexs_trans_push: ∀RN,RP. (∀L. reflexive ? (RN L)) → (∀L. ref
                              d_liftable2_sn … liftsb RN → d_liftable2_sn … liftsb RP →
                              ∀f1,K1,K2. K1 ⪤*[RN, RP, f1] K2 →
                              ∀b,f,I1,L1. ⬇*[b, f] L1.ⓘ{I1} ≘ K1 →
-                             ∀f2. f ~⊚ f1 ≘ ↑f2 →
+                             ∀f2. f ~⊚ f1 ≘ ⫯f2 →
                              ∃∃I2,L2. ⬇*[b, f] L2.ⓘ{I2} ≘ K2 & L1 ⪤*[RN, RP, f2] L2 & RP L1 I1 I2 & L1.ⓘ{I1} ≡[f] L2.ⓘ{I2}.
 #RN #RP #H1RN #H1RP #H2RN #H2RP #f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
 elim (lexs_liftable_co_dedropable_sn … H1RN H1RP H2RN H2RP … HLK1 … HK12 … Hf2) -K1 -f1 -H1RN -H1RP -H2RN -H2RP