-(* Properties with plus-iterated structural successor for closures **********)
-
-(* Note: this is used in the closure proof *)
-lemma fqup_fpbg: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂+ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H elim (fqup_inv_step_sn … H) -H
-/3 width=5 by fqus_fpbs, fpb_fqu, ex2_3_intro/
-qed.
+lemma fpbc_fpbs_fpbg (G) (L) (T):
+ ∀G1,L1,T1. ❨G1,L1,T1❩ ≻ ❨G,L,T❩ →
+ ∀G2,L2,T2. ❨G,L,T❩ ≥ ❨G2,L2,T2❩ → ❨G1,L1,T1❩ > ❨G2,L2,T2❩.
+/2 width=9 by fpbg_intro/ qed.