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diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma
index 70cfdbd71..0ddcf6eb2 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs_tc.ma
@@ -28,38 +28,38 @@ lemma lexs_tc_refl: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
 
 lemma lexs_tc_next_sn: ∀RN,RP. c_reflexive … RN →
                        ∀f,I2,L1,L2. TC … (lexs RN RP f) L1 L2 → ∀I1. RN L1 I1 I2 → 
-                       TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                       TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #f #I2 #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by lexs_next, TC_strap, inj/
 qed.
 
 lemma lexs_tc_next_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                       ∀f,I1,I2,L1. (LTC … RN) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
-                       TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                       ∀f,I1,I2,L1. (CTC … RN) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
+                       TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_refl, lexs_next, step, inj/
 qed.
 
 lemma lexs_tc_push_sn: ∀RN,RP. c_reflexive … RP →
                        ∀f,I2,L1,L2. TC … (lexs RN RP f) L1 L2 → ∀I1. RP L1 I1 I2 → 
-                       TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                       TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRP #f #I2 #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by lexs_push, TC_strap, inj/
 qed.
 
 lemma lexs_tc_push_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                       ∀f,I1,I2,L1. (LTC … RP) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
-                       TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                       ∀f,I1,I2,L1. (CTC … RP) L1 I1 I2 → ∀L2. L1 ⪤*[RN, RP, f] L2 →
+                       TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_refl, lexs_push, step, inj/
 qed.
 
-lemma lexs_tc_inj_sn: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[LTC … RN, RP, f] L2.
+lemma lexs_tc_inj_sn: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[CTC … RN, RP, f] L2.
 #RN #RP #f #L1 #L2 #H elim H -f -L1 -L2
 /3 width=1 by lexs_push, lexs_next, inj/
 qed.
 
-lemma lexs_tc_inj_dx: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[RN, LTC … RP, f] L2.
+lemma lexs_tc_inj_dx: ∀RN,RP,f,L1,L2. L1 ⪤*[RN, RP, f] L2 → L1 ⪤*[RN, CTC … RP, f] L2.
 #RN #RP #f #L1 #L2 #H elim H -f -L1 -L2
 /3 width=1 by lexs_push, lexs_next, inj/
 qed.
@@ -67,15 +67,15 @@ qed.
 (* Main properties with transitive closure **********************************)
 
 theorem lexs_tc_next: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,I1,I2,L1. (LTC … RN) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
-                      TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                      ∀f,I1,I2,L1. (CTC … RN) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
+                      TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_tc_next_sn, lexs_tc_refl, trans_TC/
 qed.
 
 theorem lexs_tc_push: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,I1,I2,L1. (LTC … RP) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
-                      TC … (lexs RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
+                      ∀f,I1,I2,L1. (CTC … RP) L1 I1 I2 → ∀L2. TC … (lexs RN RP f) L1 L2 →
+                      TC … (lexs RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #HRP #f #I1 #I2 #L1 #H elim H -I2
 /4 width=5 by lexs_tc_push_sn, lexs_tc_refl, trans_TC/
 qed.
@@ -83,7 +83,7 @@ qed.
 (* Basic_2A1: uses: TC_lpx_sn_ind *)
 theorem lexs_tc_step_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
                          ∀f,L1,L. L1 ⪤*[RN, RP, f] L → 𝐈⦃f⦄ →
-                         ∀L2. L ⪤*[RN, LTC … RP, f] L2 → L1⪤* [RN, LTC … RP, f] L2.
+                         ∀L2. L ⪤*[RN, CTC … RP, f] L2 → L1⪤* [RN, CTC … RP, f] L2.
 #RN #RP #HRP #f #L1 #L #H elim H -f -L1 -L
 [ #f #_ #Y #H -HRP >(lexs_inv_atom1 … H) -Y // ]
 #f #I1 #I #L1 #L #HL1 #HI1 #IH #Hf #Y #H
@@ -99,7 +99,7 @@ qed-.
 (* Advanced properties ******************************************************)
 
 lemma lexs_tc_dx: ∀RN,RP. s_rs_transitive_isid RN RP →
-                  ∀f. 𝐈⦃f⦄ → ∀L1,L2. TC … (lexs RN RP f) L1 L2 → L1 ⪤*[RN, LTC … RP, f] L2.
+                  ∀f. 𝐈⦃f⦄ → ∀L1,L2. TC … (lexs RN RP f) L1 L2 → L1 ⪤*[RN, CTC … RP, f] L2.
 #RN #RP #HRP #f #Hf #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by lexs_tc_step_dx, lexs_tc_inj_dx/
 qed.
@@ -107,13 +107,13 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 lemma lexs_inv_tc_sn: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,L1,L2. L1 ⪤*[LTC … RN, RP, f] L2 → TC … (lexs RN RP f) L1 L2.
+                      ∀f,L1,L2. L1 ⪤*[CTC … RN, RP, f] L2 → TC … (lexs RN RP f) L1 L2.
 #RN #RP #HRN #HRP #f #L1 #L2 #H elim H -f -L1 -L2
 /2 width=1 by lexs_tc_next, lexs_tc_push_sn, lexs_atom, inj/
 qed-.
 
 lemma lexs_inv_tc_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
-                      ∀f,L1,L2. L1 ⪤*[RN, LTC … RP, f] L2 → TC … (lexs RN RP f) L1 L2.
+                      ∀f,L1,L2. L1 ⪤*[RN, CTC … RP, f] L2 → TC … (lexs RN RP f) L1 L2.
 #RN #RP #HRN #HRP #f #L1 #L2 #H elim H -f -L1 -L2
 /2 width=1 by lexs_tc_push, lexs_tc_next_sn, lexs_atom, inj/
 qed-.