(**************************************************************************)
include "basic_2/unfold/lsstas_lsstas.ma".
-include "basic_2/computation/yprs_lift.ma".
+include "basic_2/computation/fpbs_lift.ma".
include "basic_2/computation/ygt.ma".
include "basic_2/equivalence/cpes_cpds.ma".
include "basic_2/dynamic/snv.ma".
∀G,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G, L1, T1⦄ → ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, g].
#h #g #G0 #L0 #T0 #IH #G #L1 #T1 #HLT0 #HT1 #T2 #H
-@(cprs_ind … H) -T2 /4 width=6 by ygt_yprs_trans, cprs_yprs/
+@(cprs_ind … H) -T2 /4 width=6 by ygt_fpbs_trans, cprs_fpbs/
qed-.
fact da_cprs_lpr_aux: ∀h,g,G0,L0,T0.
∀l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l →
∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ▪[h, g] l.
#h #g #G0 #L0 #T0 #IH2 #IH1 #G #L1 #T1 #HLT0 #HT1 #l #Hl #T2 #H
-@(cprs_ind … H) -T2 /4 width=10 by snv_cprs_lpr_aux, ygt_yprs_trans, cprs_yprs/
+@(cprs_ind … H) -T2 /4 width=10 by snv_cprs_lpr_aux, ygt_fpbs_trans, cprs_fpbs/
qed-.
fact da_cpcs_aux: ∀h,g,G0,L0,T0.
elim (IH1 … Hl21 … HTU … HTT2 … HL12) -IH1 -HTU -HTT2
[2: /3 width=12 by da_cprs_lpr_aux/
|3: /3 width=10 by snv_cprs_lpr_aux/
-|4: /3 width=5 by ygt_yprs_trans, cprs_yprs/
+|4: /3 width=5 by ygt_fpbs_trans, cprs_fpbs/
] -G0 -L0 -T0 -T1 -T -l1 #U2 #HTU2 #HU2
/4 width=5 by lpr_cpcs_conf, cpcs_trans, ex2_intro/
qed-.
| lapply (lsstas_da_conf … HT1T … Hl1) #Hl1l
lapply (lsstas_conf_le … HT1T … HTU1) -HTU1 // #HTU1
elim (lsstas_cprs_lpr_aux … IH3 IH2 IH1 … Hl1l … HTU1 … HTT2 L)
- /3 width=8 by ygt_yprs_trans, lsstas_yprs, monotonic_le_minus_l/ -T #U2 #HTU2 #HU12
+ /3 width=8 by ygt_fpbs_trans, lsstas_fpbs, monotonic_le_minus_l/ -T #U2 #HTU2 #HU12
/3 width=5 by cpcs_cpes, ex3_2_intro/
]
qed-.