(* *)
(**************************************************************************)
-include "basic_2/rt_computation/cpms_fpbg.ma".
+include "ground_2/lib/arith_2b.ma".
include "basic_2/rt_computation/cprs_cprs.ma".
include "basic_2/rt_computation/lprs_cpms.ma".
include "basic_2/dynamic/cnv_drops.ma".
-include "basic_2/dynamic/cnv_etc.ma".
+include "basic_2/dynamic/cnv_preserve_sub.ma".
include "basic_2/dynamic/lsubv_cnv.ma".
(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
-(* Properties with context-free parallel reduction for local environments *****)
+(* 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 * #H1 #H2 destruct //
+ elim (cpm_inv_sort1 … H2) -H2 #H #_ destruct //
| #i #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct -IH2
elim (cnv_inv_lref_drops … H1) -H1 #I #K1 #V1 #HLK1 #HV1
elim (lpr_drops_conf … HLK1 … HL12) -HL12 // #Y #H #HLK2
elim (cnv_inv_bind … H1) -H1 #HV1 #HT1
elim (cpm_inv_bind1 … H2) -H2 *
[ #V2 #T2 #HV12 #HT12 #H destruct /4 width=9 by fqup_fpbg, cnv_bind, lpr_pair/
- | #T2 #HT12 #HXT2 #H1 #H2 destruct -HV1
- /4 width=11 by fqup_fpbg, cnv_inv_lifts, lpr_pair, drops_refl, drops_drop/
+ | #X1 #HXT1 #HX1 #H1 #H2 destruct -HV1
+ /5 width=7 by cnv_inv_lifts, fqup_fpbg, fqup_zeta, drops_refl, drops_drop/
]
| #V1 #T1 #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct
elim (cnv_inv_appl … H1) -H1 #n #p #W1 #U1 #Hn #HV1 #HT1 #HVW1 #HTU1
[ #V2 #T2 #HV12 #HT12 #H destruct
lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ #HT2
- elim (cnv_cpms_strip_lpr_far … IH2 … HVW1 … HV12 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HVW1 -HV12
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HVW1 … HV12 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HVW1 -HV12
<minus_n_O <minus_O_n #XW1 #HXW1 #HXV2
- elim (cnv_cpms_strip_lpr_far … IH2 … HTU1 … HT12 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HTU1 -HT12
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HTU1 … HT12 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HTU1 -HT12
#X #H #HTU2 -IH2 -IH1 -L1 -V1 -T1
elim (cpms_inv_abst_sn … H) -H #W2 #U2 #HW12 #_ #H destruct
elim (cprs_conf … HXW1 … HW12) -W1 #W1 #HXW1 #HW21
lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
lapply (IH1 … HW120 … HL12) /2 width=1 by fqup_fpbg/ #HW20
lapply (IH1 … HT10 … HT120 … (L2.ⓛW20) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -HT10 -HT120 #HT20
- elim (cnv_cpms_strip_lpr_far … IH2 … HVW1 … HV12 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HVW1 -HV12
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HVW1 … HV12 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HVW1 -HV12
<minus_n_O <minus_O_n #XW1 #HXW1 #HXV2
- elim (cnv_cpms_strip_lpr_far … IH2 … HW130 … HW120 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HW130 -HW120
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HW130 … HW120 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HW130 -HW120
<minus_n_O #XW30 #HXW30 #HW230 -IH2 -IH1 -L1 -V1 -W10 -T10
elim (cprs_conf … HXW1 … HXW30) -W30 #W30 #HXW1 #HXW30
lapply (cpms_trans … HXV2 … HXW1) -XW1 <plus_n_O #HV2W30
lapply (IH1 … HW02 … HL12) /2 width=1 by fqup_fpbg/ #HW2
lapply (IH1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ #HV0
lapply (IH1 … HT02 (L2.ⓓW2) ?) /2 width=1 by fqup_fpbg, lpr_pair/ #HT2
- elim (cnv_cpms_strip_lpr_far … IH2 … HVW1 … HV10 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HVW1 -HV10
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HVW1 … HV10 … HL12 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HVW1 -HV10
<minus_n_O <minus_O_n #XW1 #HXW1 #HXV0
- elim (cnv_cpms_strip_lpr_far … IH2 … HTU0 … HT02 … (L2.ⓓW2) … (L2.ⓓW2)) [|*: /2 width=2 by fqup_fpbg, lpr_pair/ ] -HTU0 -HT02 -HW02
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HTU0 … HT02 … (L2.ⓓW2) … (L2.ⓓW2)) [|*: /2 width=2 by fqup_fpbg, lpr_pair/ ] -HTU0 -HT02 -HW02
#X #H #HTU2 -IH2 -IH1 -L1 -W0 -T0 -U1
elim (cpms_inv_abst_sn … H) -H #W #U2 #HW3 #_ #H destruct -U3
lapply (cnv_lifts … HV0 (Ⓣ) … (L2.ⓓW2) … HV02) /3 width=1 by drops_refl, drops_drop/ -HV0 #HV2
[ * #W2 #T2 #HW12 #HT12 #H destruct
lapply (IH1 … HW12 … HL12) /2 width=1 by fqup_fpbg/ #HW2
lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ #HT2
- lapply (cnv_cpms_trans_lpr_far … IH1 … HTU1 L1 ?) /2 width=1 by fqup_fpbg/ #HU1
- elim (cnv_cpms_strip_lpr_far … IH2 … HWU1 … HW12 … L1 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HW12
+ lapply (cnv_cpms_trans_lpr_sub … IH1 … HTU1 L1 ?) /2 width=1 by fqup_fpbg/ #HU1
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HWU1 … HW12 … L1 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HW12
<minus_n_O <minus_O_n #XW1 #HXUW1 #HXW21
- elim (cnv_cpms_strip_lpr_far … IH2 … HTU1 … HT12 … L1 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HTU1 -HT12
+ elim (cnv_cpms_strip_lpr_sub … IH2 … HTU1 … HT12 … L1 … HL12) [|*: /2 width=2 by fqup_fpbg/ ] -HTU1 -HT12
#XT1 #HXUT1 #HXT21
elim (IH2 … HXUW1 … HXUT1 … HL12 … HL12) [|*: /2 width=4 by fqup_cpms_fwd_fpbg/ ] -HXUW1 -HXUT1 -HWU1
>eq_minus_O // #W0 #H1 #H2 -IH2 -IH1 -L1 -W1 -T1 -U1
lapply (cprs_trans … HXW21 … H1) -XW1 #H1
- lapply (cpms_trans … HXT21 … H2) -XT1 <arith_l #H2
+ lapply (cpms_trans … HXT21 … H2) -XT1 <arith_l1 #H2
/2 width=3 by cnv_cast/
| #HX -IH2 -HW1 -U1
lapply (IH1 … HX … HL12) /2 width=1 by fqup_fpbg/
projects / helm.git / blobdiff