(* Advanced inversion lemmas ************************************************)
-lemma fpbg_inv_fpbu_sn: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ →
+lemma fpbg_inv_fpbu_sn: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ →
∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbg_ind_dx … H) -G1 -L1 -T1
[ #G1 #L1 #T1 * /3 width=5 by fleq_fpbs, ex2_3_intro/
(* Advanced forward lemmas **************************************************)
-lemma fpbg_fwd_fpbs: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ →
+lemma fpbg_fwd_fpbs: â\88\80h,g,G1,G2,L1,L2,T1,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ →
⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbg_ind … H) -G2 -L2 -T2
[2: #G #G2 #L #L2 #T #T2 #_ #H2 #IH1 @(fpbs_trans … IH1) -IH1 ] (**) (* full auto fails *)