-lemma lpx_cpxs_ext_trans: ∀h,G. s_rs_transitive_isid cfull (cpx_ext h G).
-#H1 #H2 #H3 #H4 #H5 #H6 #H7 #H8 #H9 #H10
-
-
-lemma tc_lfxs_inv_lex_lfeq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 →
- ∃∃L. ⦃G, L1⦄ ⊢ ⬈*[h] L & L ≡[T] L2.
-#h #G @tc_lfxs_inv_lex_lfeq //
-[ @lfpx_frees_conf
-| @lpx_cpxs_ext_trans
\ No newline at end of file
+lemma lfpxs_inv_lpxs_lfeq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈*[h, T] L2 →
+ ∃∃L. ⦃G, L1⦄ ⊢ ⬈*[h] L & L ≡[T] L2.
+/3 width=5 by lfpx_fsge_comp, lpx_cpxs_trans, lfeq_cpx_trans, tc_lfxs_inv_lex_lfeq/ qed-.