+
+(* 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-.
+