(* RESTRICTED "BIG TREE" ORDER FOR CLOSURES *********************************)
(* Advanced forward lemmas **************************************************)
+
+lemma fpbr_fwd_fpbg: ∀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 elim (fpbr_inv_fqu_fpbs … H) -H
+/2 width=5 by fqu_fpbs_fpbg/
+qed-.
+
lemma fpbr_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃≥[h, g] ⦃G2, L2, T2⦄ →
⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
/3 width=5 by fpbr_fwd_fpbg, fpbg_fwd_fpbs/