(* *)
(**************************************************************************)
-include "basic_2/rt_computation/rdsx_csx.ma".
+include "basic_2/rt_computation/rsx_csx.ma".
include "basic_2/rt_computation/fpbs_cpx.ma".
include "basic_2/rt_computation/fpbs_csx.ma".
include "basic_2/rt_computation/fsb_fpbg.ma".
∀G2,L2,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ → ≥[h] 𝐒⦃G2,L2,T2⦄.
#h #G1 #L1 #T1 #H @(csx_ind … H) -T1
#T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind (Ⓣ) … G2 L2 T2) -G2 -L2 -T2
-#G0 #L0 #T0 #IHu #H10
+#G0 #L0 #T0 #IHu #H10
lapply (fpbs_csx_conf … H10) // -HT1 #HT0
generalize in match IHu; -IHu generalize in match H10; -H10
-@(rdsx_ind … (csx_rdsx … HT0)) -L0
+@(rsx_ind … (csx_rsx … HT0)) -L0
#L0 #_ #IHd #H10 #IHu @fsb_intro
#G2 #L2 #T2 * -G2 -L2 -T2 [ -IHd -IHc | -IHu -IHd | ]
[ /4 width=5 by fpbs_fqup_trans, fqu_fqup/
| #T2 #HT02 #HnT02
- elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0
+ elim (fpbs_cpx_tneqx_trans … H10 … HT02 HnT02) -T0
/3 width=4 by/
| #L2 #HL02 #HnL02 @(IHd … HL02 HnL02) -IHd -HnL02 [ -IHu -IHc | ]
[ /3 width=3 by fpbs_lpxs_trans, lpx_lpxs/
| #G3 #L3 #T3 #H03 #_
elim (lpx_fqup_trans … H03 … HL02) -L2 #L4 #T4 #HT04 #H43 #HL43
- elim (tdeq_dec T0 T4) [ -IHc -HT04 #HT04 | -IHu #HnT04 ]
- [ elim (tdeq_fqup_trans … H43 … HT04) -T4 #L2 #T4 #H04 #HT43 #HL24
- /4 width=7 by fsb_fpbs_trans, tdeq_rdeq_lpx_fpbs, fpbs_fqup_trans/
- | elim (cpxs_tdneq_fwd_step_sn … HT04 HnT04) -HT04 -HnT04 #T2 #T5 #HT02 #HnT02 #HT25 #HT54
- elim (fpbs_cpx_tdneq_trans … H10 … HT02 HnT02) -T0 #T0 #HT10 #HnT10 #H02
- /3 width=14 by fpbs_cpxs_tdeq_fqup_lpx_trans/
+ elim (teqx_dec T0 T4) [ -IHc -HT04 #HT04 | -IHu #HnT04 ]
+ [ elim (teqx_fqup_trans … H43 … HT04) -T4 #L2 #T4 #H04 #HT43 #HL24
+ /4 width=7 by fsb_fpbs_trans, teqx_reqx_lpx_fpbs, fpbs_fqup_trans/
+ | elim (cpxs_tneqx_fwd_step_sn … HT04 HnT04) -HT04 -HnT04 #T2 #T5 #HT02 #HnT02 #HT25 #HT54
+ elim (fpbs_cpx_tneqx_trans … H10 … HT02 HnT02) -T0 #T0 #HT10 #HnT10 #H02
+ /3 width=14 by fpbs_cpxs_teqx_fqup_lpx_trans/
]
]
]