+(* Basic properties *********************************************************)
+
+lemma fpb_fpbsa_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 * -G -L -T [ #G #L #T #HG1 | #T #HT1 | #L #HL1 ]
+#G2 #L2 #T2 * #L0 #T0 #HT0 #HG2 #L2
+[ elim (fsupq_cpxs_trans … HT0 … HG1) -T
+ /3 width=7 by fsups_trans, ex3_2_intro/
+| /3 width=5 by cpxs_strap2, ex3_2_intro/
+| lapply (lpx_cpxs_trans … HT0 … HL1) -HT0 #HT10
+]
+
+(* 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_dx … H) -G1 -L1 -T1
+/2 width=5 by fpb_fpbsa_trans, ex3_2_intro/
+qed.
+