-
-lemma fpbs_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ ∨
- ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
-[ /2 width=1 by or_introl/
-| #G #G2 #L #L2 #T #T2 #_ #H2 * #H1 elim (fpb_fpbu … H2) -H2 #H2
- [ /3 width=5 by fleq_trans, or_introl/
- | /5 width=5 by fpbc_fpbg, fleq_fpbc_trans, fpbu_fpbc, or_intror/
- | /3 width=5 by fpbg_fleq_trans, or_intror/
- | /4 width=5 by fpbg_strap1, fpbu_fpbc, or_intror/
- ]
-]
-qed-.