-lemma lfdeq_atom: ∀h,o,I. ⋆ ≛[h, o, ⓪{I}] ⋆.
+lemma tdeq_lfxs_div (R) (h) (o): ∀T1,T2. T1 ≛[h, o] T2 →
+ ∀L1,L2. L1 ⪤*[R, T2] L2 → L1 ⪤*[R, T1] L2.
+/3 width=5 by tdeq_lfxs_conf, tdeq_sym/ qed-.
+
+lemma tdeq_lfdeq_conf (h) (o): s_r_confluent1 … (cdeq h o) (lfdeq h o).
+/2 width=5 by tdeq_lfxs_conf/ qed-.
+
+lemma tdeq_lfdeq_div (h) (o): ∀T1,T2. T1 ≛[h, o] T2 →
+ ∀L1,L2. L1 ≛[h, o, T2] L2 → L1 ≛[h, o, T1] L2.
+/2 width=5 by tdeq_lfxs_div/ qed-.
+
+lemma lfdeq_atom (h) (o): ∀I. ⋆ ≛[h, o, ⓪{I}] ⋆.