+(* Advanced properties ******************************************************)
+
+lemma tdeq_fpbs_trans: ∀h,T1,T. T1 ≛ T →
+ ∀G1,G2,L1,L2,T2. ⦃G1,L1,T⦄ ≥[h] ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
+/3 width=5 by fdeq_fpbs_trans, tdeq_fdeq/ qed-.
+
+lemma fpbs_tdeq_trans: ∀h,G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T⦄ →
+ ∀T2. T ≛ T2 → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
+/3 width=5 by fpbs_fdeq_trans, tdeq_fdeq/ qed-.
+