-lemma fpbg_fqu_trans (h): ∀G1,G,G2,L1,L,L2,T1,T,T2.
- ⦃G1,L1,T1⦄ >[h] ⦃G,L,T⦄ → ⦃G,L,T⦄ ⬂ ⦃G2,L2,T2⦄ →
- ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄.
-#h #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
-/4 width=5 by fpbg_fpbq_trans, fpbq_fquq, fqu_fquq/
+lemma fpbg_intro (G3) (G4) (L3) (L4) (T3) (T4):
+ ∀G1,L1,T1,G2,L2,T2.
+ ❪G1,L1,T1❫ ≥ ❪G3,L3,T3❫ → ❪G3,L3,T3❫ ≻ ❪G4,L4,T4❫ →
+ ❪G4,L4,T4❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+/2 width=9 by ex3_6_intro/ qed.
+
+(* Basic_2A1: was: fpbg_fpbq_trans *)
+lemma fpbg_fpb_trans:
+ ∀G1,G,G2,L1,L,L2,T1,T,T2.
+ ❪G1,L1,T1❫ > ❪G,L,T❫ → ❪G,L,T❫ ≽ ❪G2,L2,T2❫ →
+ ❪G1,L1,T1❫ > ❪G2,L2,T2❫.
+#G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
+elim (fpbg_inv_gen … H1) -H1
+/3 width=13 by fpbs_strap1, fpbg_intro/