-lemma fpbs_fqup_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G,L,T⦄ →
- ∀G2,L2,T2. ⦃G,L,T⦄ ⬂+ ⦃G2,L2,T2⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-/3 width=5 by fpbs_fqus_trans, fqup_fqus/ qed-.
-
-lemma fqup_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ⦃G,L,T⦄ ≥[h] ⦃G2,L2,T2⦄ →
- ∀G1,L1,T1. ⦃G1,L1,T1⦄ ⬂+ ⦃G,L,T⦄ → ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-/3 width=5 by fqus_fpbs_trans, fqup_fqus/ qed-.
+lemma fpbs_fqup_trans:
+ ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
+ ∀G2,L2,T2. ❪G,L,T❫ ⬂+ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+#G1 #G #L1 #L #T1 #T #H1 #G2 #L2 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
+/3 width=5 by fpbs_strap1, fqu_fpb/
+qed-.
+
+lemma fqup_fpbs_trans:
+ ∀G,G2,L,L2,T,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ →
+ ∀G1,L1,T1. ❪G1,L1,T1❫ ⬂+ ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+#G #G2 #L #L2 #T #T2 #H1 #G1 #L1 #T1 #H @(fqup_ind_dx … H) -G1 -L1 -T1
+/3 width=9 by fpbs_strap2, fqu_fpb/
+qed-.
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