+(* Basic properties *********************************************************)
+
+lemma fpbsa_fpb_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G, L, T⦄ →
+ ∀G2,L2,T2. ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #L1 #L #T1 #T * #L0 #T0 #H10 #HT0 #HL0 #G2 #L2 #T2 * -G2 -L2 -T2
+[ #G2 #L2 #T2 #H2
+| /4 width=7 by lpxs_cpx_trans, cpxs_trans, ex3_2_intro/
+| /3 width=7 by lpxs_strap1, ex3_2_intro/
+]
+
+(* Main properties **********************************************************)
+
+theorem fpbs_fpbsa: ∀h,g,G1,G2,L1,L2,T1,T2.
+ ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥≥[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
+/2 width=5 by fpbsa_fpb_trans, ex3_2_intro/
+qed.
+