(* PROPER PARALLEL RST-COMPUTATION FOR CLOSURES *****************************)
-(* Properties with plus-iterated structural successor for closures **********)
+(* Advanced properties ******************************************************)
-(* Note: this is used in the closure proof *)
-lemma fqup_fpbg: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, o] ⦃G2, L2, T2⦄.
-#h #o #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_fpbg (G1) (G2) (L1) (L2) (T1) (T2):
+ ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+/3 width=13 by fpbg_intro, fpb_fpbs/ 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.