(* *)
(**************************************************************************)
-include "basic_2/equivalence/lsubss_ssta.ma".
+include "basic_2/computation/cpds_cpds.ma".
include "basic_2/dynamic/snv_cpcs.ma".
+include "basic_2/dynamic/lsubsv_ssta.ma".
(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
(* Properties on sn parallel reduction for local environments ***************)
-fact ssta_cpr_lpr_aux: ∀h,g,L0,T0.
- (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
- (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
- (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) →
- ∀L1,T1. L0 = L1 → T0 = T1 → IH_ssta_cpr_lpr h g L1 T1.
-#h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 * * [|||| *]
-[ #k #_ #_ #_ #X2 #l #H2 #X3 #H3 #L2 #HL12 -IH3 -IH2 -IH1
+fact ssta_cpr_lpr_aux: ∀h,g,G0,L0,T0.
+ (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_ssta h g G1 L1 T1) →
+ (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) →
+ (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_ssta_cpr_lpr h g G1 L1 T1) →
+ ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_ssta_cpr_lpr h g G1 L1 T1.
+#h #g #G0 #L0 #T0 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| *]
+[ #k #_ #_ #_ #_ #X2 #l #H2 #X3 #H3 #L2 #HL12 -IH3 -IH2 -IH1
elim (ssta_inv_sort1 … H2) -H2 #Hkl #H destruct
>(cpr_inv_sort1 … H3) -X3 /4 width=6/
-| #i #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2
+| #i #HG0 #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2
elim (snv_inv_lref … H1) -H1 #I0 #K0 #V0 #H #HV1
elim (ssta_inv_lref1 … H2) -H2 * #K1
#V1 #W1 [| #l0 ] #HLK1 #HVW1 #HWU1 [| #H destruct ]
lapply (ldrop_mono … H … HLK1) -H #H destruct
- lapply (ldrop_pair2_fwd_fw … HLK1 (#i)) #HKV1
+ lapply (fsupp_lref … G1 … HLK1) #HKV1
elim (lpr_ldrop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
elim (lpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
lapply (ldrop_fwd_ldrop2 … HLK2) #H2
lapply (ssta_lift … HVW2 … H2 … HW0 … HWU2) -HVW2 -HW0
lapply (cpcs_lift … H2 … HWU1 … HWU2 HW12) -H2 -W1 /3 width=6/
]
-| #p #_ #HT0 #H1 destruct -IH3 -IH2 -IH1
+| #p #_ #_ #HT0 #H1 destruct -IH3 -IH2 -IH1
elim (snv_inv_gref … H1)
-| #a #I #V1 #T1 #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2
+| #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2
elim (snv_inv_bind … H1) -H1 #_ #HT1
elim (ssta_inv_bind1 … H2) -H2 #U1 #HTU1 #H destruct
elim (cpr_inv_bind1 … H3) -H3 *
lapply (cpcs_bind1 true … V1 V1 … HU12) // -HU12 #HU12
lapply (cpcs_cpr_strap1 … HU12 U ?) -HU12 /2 width=3/
]
-| #V1 #T1 #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct
+| #V1 #T1 #HG0 #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct
elim (snv_inv_appl … H1) -H1 #a #W1 #W10 #U10 #l0 #HV1 #HT1 #HVW1 #HW10 #HTU10
elim (ssta_inv_appl1 … H2) -H2 #U1 #HTU1 #H destruct
elim (cpr_inv_appl1 … H3) -H3 *
[ #V2 #T2 #HV12 #HT12 #H destruct -a -l0 -W1 -W10 -U10 -HV1 -IH3 -IH2
elim (IH1 … HTU1 … HT12 … HL12) -IH1 -HTU1 // [2: /2 width=1/ ] -T1 #U2 #HTU2 #HU12
lapply (lpr_cpr_conf … HL12 … HV12) -L1 /3 width=5/
- | #b #V2 #W #T2 #T20 #HV12 #HT20 #H1 #H2 destruct
- elim (snv_inv_bind … HT1) -HT1 #HW #HT2
+ | #b #V2 #W2 #W20 #T2 #T20 #HV12 #HW20 #HT20 #H1 #H2 destruct
+ elim (snv_inv_bind … HT1) -HT1 #HW2 #HT2
elim (ssta_inv_bind1 … HTU1) -HTU1 #U2 #HTU2 #H destruct
- elim (dxprs_inv_abst1 … HTU10) -HTU10 #W0 #U0 #HW0 #_ #H destruct
- lapply (cprs_div … HW10 … HW0) -W0 #HW1W
+ elim (cpds_inv_abst1 … HTU10) -HTU10 #W0 #U0 #HW0 #_ #H destruct
+ lapply (cprs_div … HW10 … HW0) -W0 #HW12
elim (ssta_fwd_correct … HVW1) <minus_plus_m_m #X1 #HWX1
- elim (snv_fwd_ssta … HW) #l1 #V #HWV
+ elim (snv_fwd_ssta … HW2) #l1 #V22 #HWV22
lapply (IH3 … HVW1) -IH3 // [ /2 width=1/ ] #HW1
- elim (ssta_cpcs_lpr_aux … IH2 IH1 … HWX1 … HWV … L1) -IH2 -HWX1 //
+ elim (ssta_cpcs_lpr_aux … IH2 IH1 … HWX1 … HWV22 … L1) -HWX1 //
[2: /2 width=1/
- |3: /4 width=4 by ygt_yprs_trans, fw_ygt, sstas_yprs, ssta_sstas/
+ |3: /4 width=5 by ygt_yprs_trans, fsupp_ygt, sstas_yprs, ssta_sstas/
] #H #_ destruct -X1
- elim (IH1 … HVW1 … HV12 … HL12) -HVW1 // -HV1 [2: /2 width=1/ ] #W2 #HVW2 #HW12
- elim (IH1 … HWV W … HL12) -HWV // -HW [2: /2 width=1/ ] #V0 #HWV0 #_
- elim (IH1 … HTU2 … HT20 (L2.ⓛW)) -IH1 -HTU2 -HT20 // [2,3: /2 width=1/ ] -HT2 #U20 #HTU20 #HU20
- lapply (cpcs_lpr_conf … HL12 … HW1W) #HW1W
+ lapply (IH2 … HV1 … HV12 … HL12) [ /2 width=1/ ] #HV2
+ lapply (IH2 … HW2 … HW20 … HL12) [ /2 width=1/ ] -IH2 #H2W20
+ elim (IH1 … HVW1 … HV12 … HL12) -HVW1 // -HV1 [2: /2 width=1/ ] #W12 #HVW12 #HW112
+ elim (IH1 … HWV22 … HW20 … HL12) -HWV22 // -HW2 [2: /2 width=1/ ] #V20 #HWV20 #_
+ elim (IH1 … HTU2 … HT20 (L2.ⓛW20)) -IH1 -HTU2 -HT20 // [2,3: /2 width=1/ ] -HT2 #U20 #HTU20 #HU20
+ lapply (lpr_cpcs_conf … HL12 … HW12) -HW12 #HW12
+ lapply (lpr_cpr_conf … HL12 … HW20) -HW20 #HW20
lapply (lpr_cpr_conf … HL12 … HV12) -L1 #HV12
- lapply (cpcs_ext_bind … HV12 … HU20 b Abbr) -HV12 -HU20 #HU20
- lapply (cpcs_canc_sn … HW12 HW1W) -W1 #HW2
- elim (lsubss_ssta_trans … HTU20 (L2.ⓓV2) ?) -HTU20
- [ #U #HTU20 #HUU20 -HWV0 -W2
- lapply (cpcs_bind1 b … V2 V2 … HUU20) // -HUU20 #HUU20
- lapply (cpcs_canc_dx … HU20 … HUU20) -U20 #HU2
- lapply (cpcs_cpr_strap2 … (ⓐV1.ⓛ{b}W.U2) … HU2) [ /2 width=1/ ] /3 width=3/
- | -b -l -V -V1 -T2 -T20 -U0 -U2 -U20 /2 width=6/
+ lapply (cpcs_canc_sn … HW12 HW112) -W1 #HW12
+ lapply (cpcs_canc_sn … HW12 HW20) -HW12 #HW12
+ elim (lsubsv_ssta_trans … HTU20 (L2.ⓓⓝW20.V2)) -HTU20
+ [ #U #HTU20 #HUU20 -HVW12 -HWV20 -HW12
+ @(ex2_intro … (ⓓ{b}ⓝW20.V2.U)) [ /3 width=1/ ] -HTU20
+ @(cpcs_canc_dx … (ⓓ{b}ⓝW20.V2.U20)) [2: /2 width=1/ ] -HUU20
+ @(cpcs_cpr_strap1 … (ⓐV2.ⓛ{b}W20.U20)) [2: /2 width=1/ ]
+ /3 by cpcs_bind2, cpcs_flat/
+ | -HU20 -HW20 -HV12 /3 width=5 by lsubsv_abbr, snv_cast/
]
| #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -a -l0 -W1 -W10 -HV1 -IH3 -IH2
elim (ssta_inv_bind1 … HTU1) -HTU1 #U0 #HTU0 #H destruct
lapply (cpcs_flat … HV10 … HU02 Appl) -HV10 -HU02 #HU02
lapply (cpcs_cpr_strap1 … HU02 (ⓓ{b}W2.ⓐV2.U2) ?) [ /2 width=3/ ] -V0 /4 width=3/
]
-| #U0 #T1 #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2
+| #U0 #T1 #HG0 #HL0 #HT0 #H1 #X2 #l #H2 #X3 #H3 #L2 #HL12 destruct -IH3 -IH2
elim (snv_inv_cast … H1) -H1 #T0 #l0 #_ #HT1 #HT10 #_
lapply (ssta_inv_cast1 … H2) -H2 #HTU1
elim (ssta_mono … HT10 … HTU1) -HT10 #H1 #H2 destruct
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