(**************************************************************************)
include "ground_2/lib/arith_2b.ma".
-include "basic_2/rt_computation/cpms_fpbg.ma".
include "basic_2/rt_computation/cprs_cprs.ma".
include "basic_2/rt_computation/lprs_cpms.ma".
include "basic_2/dynamic/cnv_drops.ma".
(* Sub preservation propery with t-bound rt-transition for terms ************)
-fact cnv_cpm_trans_lpr_aux (a) (h) (o):
+fact cnv_cpm_trans_lpr_aux (a) (h):
∀G0,L0,T0.
- (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
- (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
+ (∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
+ (∀G1,L1,T1. ⦃G0,L0,T0⦄ >[h] ⦃G1,L1,T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_trans_lpr a h G1 L1 T1.
-#a #h #o #G0 #L0 #T0 #IH2 #IH1 #G1 #L1 * * [|||| * ]
+#a #h #G0 #L0 #T0 #IH2 #IH1 #G1 #L1 * * [|||| * ]
[ #s #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #_ destruct -IH2 -IH1 -H1
elim (cpm_inv_sort1 … H2) -H2 #H #_ destruct //
| #i #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct -IH2
lapply (cpms_trans … HXV2 … HXW1) -XW1 <plus_n_O #HV2W1
lapply (cpms_trans … HTU2 … (ⓛ{p}W1.U2) ?)
[3:|*: /2 width=2 by cpms_bind/ ] -W2 <plus_n_O #HTU2
- /4 width=7 by cnv_appl, minus_le_trans_sn/
+ /3 width=7 by cnv_appl, le_ylt_trans/
| #q #V2 #W10 #W20 #T10 #T20 #HV12 #HW120 #HT120 #H1 #H2 destruct
elim (cnv_inv_bind … HT1) -HT1 #HW10 #HT10
elim (cpms_inv_abst_sn … HTU1) -HTU1 #W30 #T30 #HW130 #_ #H destruct -T30
elim (cprs_conf … HXW32 … HW3) -W3 #W3 #HXW23 #HW3
lapply (cpms_trans … HXVW2 … HXW23) -XW2 <plus_n_O #H1
lapply (cpms_trans … HTU2 ? (ⓛ{p}W3.U2) ?) [3:|*:/2 width=2 by cpms_bind/ ] -W #H2
- /5 width=7 by cnv_appl, cnv_bind, minus_le_trans_sn/
+ /4 width=7 by cnv_appl, cnv_bind, le_ylt_trans/
]
| #W1 #T1 #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct
elim (cnv_inv_cast … H1) -H1 #U1 #HW1 #HT1 #HWU1 #HTU1