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diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.ma
index bb3aec919..d9112a12e 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lex_tc.ma
@@ -16,10 +16,19 @@ include "basic_2/syntax/ext2_tc.ma".
 include "basic_2/relocation/lexs_tc.ma".
 include "basic_2/relocation/lex.ma".
 
+alias symbol "subseteq" = "relation inclusion".
+
 (* GENERIC EXTENSION OF A CONTEXT-SENSITIVE REALTION FOR TERMS **************)
 
 (* Inversion lemmas with transitive closure *********************************)
 
+(* Basic_2A1: was: lpx_sn_LTC_TC_lpx_sn *)
+lemma lex_inv_ltc: ∀R. c_reflexive … R →
+                   lex (LTC … R) ⊆ TC … (lex R).
+#R #HR #L1 #L2 *
+/5 width=11 by lexs_inv_tc_dx, lexs_co, ext2_inv_tc, ext2_refl, monotonic_TC, ex2_intro/
+qed-.
+
 lemma s_rs_transitive_lex_inv_isid: ∀R. s_rs_transitive … R (λ_.lex R) →
                                     s_rs_transitive_isid cfull (cext2 R).
 #R #HR #f #Hf #L2 #T1 #T2 #H #L1 #HL12
@@ -30,3 +39,25 @@ elim (ext2_tc … H) -H
   @(HR … HV12) -HV12 /2 width=3 by ex2_intro/ (**) (* auto fails *)
 ]
 qed-.
+
+(* Properties with transitive closure ***************************************)
+
+(* Basic_2A1: was: TC_lpx_sn_inv_lpx_sn_LTC *)
+lemma lex_ltc: ∀R. s_rs_transitive … R (λ_. lex R) →
+               TC … (lex R) ⊆ lex (LTC … R).
+#R #HR #L1 #L2 #HL12
+lapply (monotonic_TC … (lexs cfull (cext2 R) 𝐈𝐝) … HL12) -HL12
+[ #L1 #L2 * /3 width=3 by lexs_eq_repl_fwd, eq_id_inv_isid/
+| /5 width=9 by s_rs_transitive_lex_inv_isid, lexs_tc_dx, lexs_co, ext2_tc, ex2_intro/
+]
+qed-.
+
+lemma lex_ltc_step_dx: ∀R. c_reflexive … R → s_rs_transitive … R (λ_. lex R) →
+                       ∀L1,L. lex (LTC … R) L1 L →
+                       ∀L2. lex R L L2 → lex (LTC … R) L1 L2.
+/4 width=3 by lex_ltc, lex_inv_ltc, step/ qed-.
+
+lemma lex_ltc_step_sn: ∀R. c_reflexive … R → s_rs_transitive … R (λ_. lex R) →
+                       ∀L1,L. lex R L1 L →
+                       ∀L2. lex (LTC … R) L L2 → lex (LTC … R) L1 L2.
+/4 width=3 by lex_ltc, lex_inv_ltc, TC_strap/ qed-.