#T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind … G2 L2 T2) -G2 -L2 -T2
#G0 #L0 #T0 #IHu #H10 lapply (csx_fpbs_conf … H10) // -HT1
#HT0 generalize in match IHu; -IHu generalize in match H10; -H10
-@(lsx_ind … (csx_lsx … HT0 0)) -L0
+@(lsx_ind_alt … (csx_lsx … HT0 0)) -L0
#L0 #_ #IHl #H10 #IHu @fsb_intro
#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHl -IHc | -IHu -IHl | ]
[ /3 width=5 by fpbs_fqup_trans/
lemma csx_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
(∀G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, g] T1 →
- (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\8b\95[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+ (â\88\80G2,L2,T2. â¦\83G1, L1, T1â¦\84 >â\89¡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
R G1 L1 T1
) →
∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R G L T.