include "basic_2/computation/fsb_alt.ma".
(* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
include "basic_2/computation/fsb_alt.ma".
(* "BIG TREE" STRONGLY NORMALIZING TERMS ************************************)
#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
#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
#L0 #_ #IHl #H10 #IHu @fsb_intro
#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHl -IHc | -IHu -IHl | ]
[ /3 width=5 by fpbs_fqup_trans/
| #T2 #HT02 #HnT02 elim (fpbs_cpxs_trans_neq … H10 … HT02 HnT02) -T0
/3 width=4 by/
| #L2 #HL02 #HnL02 @(IHl … HL02 HnL02) -IHl -HnL02 [ -IHu -IHc | ]
#L0 #_ #IHl #H10 #IHu @fsb_intro
#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHl -IHc | -IHu -IHl | ]
[ /3 width=5 by fpbs_fqup_trans/
| #T2 #HT02 #HnT02 elim (fpbs_cpxs_trans_neq … H10 … HT02 HnT02) -T0
/3 width=4 by/
| #L2 #HL02 #HnL02 @(IHl … HL02 HnL02) -IHl -HnL02 [ -IHu -IHc | ]