(* *)
(**************************************************************************)
-include "basic_2/computation/cpds_cpds.ma".
include "basic_2/dynamic/snv_aaa.ma".
-include "basic_2/dynamic/snv_cpcs.ma".
+include "basic_2/dynamic/snv_cpes.ma".
include "basic_2/dynamic/lsubsv_lstas.ma".
(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
/5 width=8 by cpcs_cpr_strap1, cpcs_bind1, cpr_zeta, drop_drop, ex2_intro/
]
| #V1 #T1 #HG0 #HL0 #HT0 #H1 #l1 #l2 #Hl21 #Hl1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct
- elim (snv_inv_appl … H1) -H1 #a #W1 #W10 #U10 #l0 #HV1 #HT1 #Hl0 #HVW1 #HW10 #HTU10
+ elim (snv_inv_appl … H1) -H1 #a #W1 #U1 #l0 #HV1 #HT1 #HVW1 #HTU1
lapply (da_inv_flat … Hl1) -Hl1 #Hl1
- elim (lstas_inv_appl1 … H2) -H2 #U1 #HTU1 #H destruct
+ elim (lstas_inv_appl1 … H2) -H2 #X #HT1U #H destruct
elim (cpr_inv_appl1 … H3) -H3 *
- [ #V2 #T2 #HV12 #HT12 #H destruct -a -l0 -W1 -W10 -U10 -HV1 -IH4 -IH3 -IH2
- elim (IH1 … Hl1 … HTU1 … HT12 … HL12) -IH1 -Hl1 -HTU1
+ [ #V2 #T2 #HV12 #HT12 #H destruct -a -l0 -W1 -U1 -HV1 -IH4 -IH3 -IH2
+ elim (IH1 … Hl1 … HT1U … HT12 … HL12) -IH1 -Hl1 -HT1U
/4 width=5 by fqup_fpbg, cpcs_flat, lpr_cpr_conf, lstas_appl, ex2_intro/
| #b #V2 #W2 #W3 #T2 #T3 #HV12 #HW23 #HT23 #H1 #H2 destruct
elim (snv_inv_bind … HT1) -HT1 #HW2 #HT2
lapply (da_inv_bind … Hl1) -Hl1 #Hl1
- elim (lstas_inv_bind1 … HTU1) -HTU1 #U2 #HTU2 #H destruct
- elim (cpds_inv_abst1 … HTU10) -HTU10 #W0 #U0 #HW20 #_ #H destruct
- lapply (cprs_div … HW10 … HW20) -W0 #HW12
- lapply (da_sta_conf … HVW1 … Hl0) <minus_plus_m_m #H
- elim (snv_fwd_da … HW2) #l #Hl
- lapply (IH4 … HV1 … 1 … Hl0 W1 ?) /2 width=1 by fqup_fpbg, sta_lstas/ #HW1
- lapply (da_cpcs_aux … IH3 IH2 … H … Hl … HW12) // -H
- /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, sta_fpbs/ #H destruct
- lapply (IH3 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
- lapply (IH2 … Hl0 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2l
- elim (IH1 … 1 … Hl0 … W1 … HV12 … HL12) /2 width=1 by fqup_fpbg, sta_lstas/ -HVW1 #W4 #H #HW14
- lapply (lstas_inv_SO … H) #HV2W4
- lapply (da_sta_conf … HV2W4 … HV2l) <minus_plus_m_m #HW4l
- lapply (IH4 … HV2 … HV2l … H) -H /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs/ #HW4
+ elim (lstas_inv_bind1 … HT1U) -HT1U #U #HT2U #H destruct
+ elim (cpds_inv_abst1 … HTU1) -HTU1 #W0 #U0 #HW20 #_ #H destruct -U0 -l0
+ elim (snv_fwd_da … HW2) #l0 #HW2l
+ lapply (cpds_div … W2 … 0 … HVW1) /2 width=3 by cprs_cpds/ -W0 #H21
+ elim (snv_fwd_da … HV1) #l #HV1l
+ elim (da_cpes_aux … IH4 IH3 IH2 … HW2l … HV1l … H21) /2 width=1 by fqup_fpbg/ #_ #H
+ <minus_n_O #H0 destruct >(plus_minus_m_m l 1) in HV1l; // -H #HV1l
+ lapply (cpes_cpr_lpr_aux … IH2 IH1 … H21 … HW23 … HV12 … HL12) -H21 /2 width=1 by fqup_fpbg/ #H32
lapply (IH3 … HW23 … HL12) /2 width=1 by fqup_fpbg/ #HW3
- lapply (IH2 … Hl … HW23 … HL12) /2 width=1 by fqup_fpbg/ #HW3l
- elim (IH1 … Hl1 … HTU2 … HT23 (L2.ⓛW3)) -HTU2 /2 width=1 by fqup_fpbg, lpr_pair/ #U3 #HTU3 #HU23
- lapply (cpcs_cpr_strap1 … HW12 … HW23) #H
- lapply (lpr_cpcs_conf … HL12 … H) -H #H
- lapply (cpcs_canc_sn … HW14 H) -H #HW43
+ lapply (IH3 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
+ lapply (IH2 … HW2l … HW23 … HL12) /2 width=1 by fqup_fpbg/ -HW2 -HW2l #HW3l
+ lapply (IH2 … HV1l … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HV1 -HV1l #HV2l
+ elim (IH1 … Hl1 … HT2U … HT23 (L2.ⓛW3)) -HT2U /2 width=1 by fqup_fpbg, lpr_pair/ #U3 #HTU3 #HU23
elim (lsubsv_lstas_trans … g … HTU3 … Hl21 … (L2.ⓓⓝW3.V2)) -HTU3
- [ #U4 #HT3U4 #HU43 -HW12 -HW3 -HW3l -W4 -IH2 -IH3 -IH4
+ [ #U4 #HT3U4 #HU43 -IH1 -IH2 -IH3 -IH4 -l -l1 -HW3 -HV2 -HT2
@(ex2_intro … (ⓓ{b}ⓝW3.V2.U4)) /2 width=1 by lstas_bind/ -HT3U4
@(cpcs_canc_dx … (ⓓ{b}ⓝW3.V2.U3)) /2 width=1 by cpcs_bind_dx/ -HU43
@(cpcs_cpr_strap1 … (ⓐV2.ⓛ{b}W3.U3)) /2 width=1 by cpr_beta/
/4 width=3 by cpcs_flat, cpcs_bind2, lpr_cpr_conf/
| -U3
- @(lsubsv_beta … l) /3 width=7 by fqup_fpbg/
- #W #W0 #l0 #Hl0 #HV2W #HW30
- lapply (lstas_sta_conf_pos … HV2W4 … HV2W) -HV2W #HW4W
- @(lstas_cpcs_lpr_aux … IH3 IH2 IH1 … Hl0 … HW4W … Hl0 … HW30 … HW43) //
- [ /3 width=9 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_sta_fpbs/
- | /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs/
- ]
+ @(lsubsv_beta … (l-1)) /3 width=7 by fqup_fpbg/
+ @hsnv_cast [1,2: // ] #l0 #Hl0
+ lapply (cpes_le_aux … IH4 IH3 IH2 IH1 … HW3l … HV2l … l0 … H32) -IH4 -IH3 -IH2 -IH1 -HW3l -HV2l -H32
+ /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs, le_S_S/
| -IH1 -IH3 -IH4 /3 width=9 by fqup_fpbg, lpr_pair/
]
- | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -a -l0 -W1 -W10 -HV1 -IH4 -IH3 -IH2
+ | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -a -l0 -W1 -HV1 -IH4 -IH3 -IH2
elim (snv_inv_bind … HT1) -HT1 #_ #HT0
lapply (da_inv_bind … Hl1) -Hl1 #Hl1
- elim (lstas_inv_bind1 … HTU1) -HTU1 #U0 #HTU0 #H destruct
+ elim (lstas_inv_bind1 … HT1U) -HT1U #U0 #HTU0 #H destruct
elim (IH1 … Hl1 … HTU0 … HT02 (L2.ⓓW2)) -IH1 -Hl1 -HTU0 /2 width=1 by fqup_fpbg, lpr_pair/ -T0 #U2 #HTU2 #HU02
lapply (lpr_cpr_conf … HL12 … HV10) -HV10 #HV10
lapply (lpr_cpr_conf … HL12 … HW02) -L1 #HW02
]
| #W1 #T1 #HG0 #HL0 #HT0 #H1 #l1 #l2 @(nat_ind_plus … l2) -l2 [ #_ | #l2 #_ #Hl21 ] #Hl1 #X2 #H2 #X3 #H3 #L2 #HL12 destruct -IH4 -IH3 -IH2
[ lapply (lstas_inv_O … H2) -H2 #H destruct -IH1 -H1 -l1 /4 width=5 by lpr_cpcs_conf, cpr_cpcs_dx, ex2_intro/ ]
- elim (snv_inv_cast … H1) -H1 #U1 #l #_ #HT1 #_ #_ #_ -U1 -l
+ elim (snv_inv_cast … H1) -H1 #U1 #_ #HT1 #_ #_ -U1
lapply (da_inv_flat … Hl1) -Hl1 #Hl1
lapply (lstas_inv_cast1 … H2) -H2 #HTU1
elim (cpr_inv_cast1 … H3) -H3
[ * #U2 #T2 #_ #HT12 #H destruct
elim (IH1 … Hl1 … HTU1 … HT12 … HL12) -IH1 -Hl1 -HTU1 -HL12
/3 width=3 by fqup_fpbg, lstas_cast, ex2_intro/
- | #HT1X3
- elim (IH1 … Hl1 … HTU1 … HT1X3 … HL12) -IH1 -Hl1 -HTU1 -HL12
+ | #HT1X3 elim (IH1 … Hl1 … HTU1 … HT1X3 … HL12) -IH1 -Hl1 -HTU1 -HL12
/2 width=3 by fqup_fpbg, ex2_intro/
]
]
projects / helm.git / blobdiff