--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2A/dynamic/snv_lift.ma".
+include "basic_2A/dynamic/snv_aaa.ma".
+include "basic_2A/dynamic/snv_scpes.ma".
+include "basic_2A/dynamic/lsubsv_snv.ma".
+
+(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
+
+(* Properties on context-free parallel reduction for local environments *****)
+
+fact snv_cpr_lpr_aux: ∀h,g,G0,L0,T0.
+ (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_lstas h g G1 L1 T1) →
+ (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_lstas_cpr_lpr h g G1 L1 T1) →
+ (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_da_cpr_lpr 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 = G1 → L0 = L1 → T0 = T1 → IH_snv_cpr_lpr h g G1 L1 T1.
+#h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ]
+[ #k #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #_ destruct -IH4 -IH3 -IH2 -IH1 -H1
+ >(cpr_inv_sort1 … H2) -X //
+| #i #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2
+ elim (snv_inv_lref … H1) -H1 #I #K1 #V1 #HLK1 #HV1
+ elim (lpr_drop_conf … HLK1 … HL12) -HL12 #X #H #HLK2
+ elim (lpr_inv_pair1 … H) -H #K2 #V2 #HK12 #HV12 #H destruct
+ lapply (fqup_lref … G1 … HLK1) #HKL
+ elim (cpr_inv_lref1 … H2) -H2
+ [ #H destruct -HLK1 /4 width=10 by fqup_fpbg, snv_lref/
+ | * #K0 #V0 #W0 #H #HVW0 #W0 -HV12
+ lapply (drop_mono … H … HLK1) -HLK1 -H #H destruct
+ lapply (drop_fwd_drop2 … HLK2) -HLK2 /4 width=8 by fqup_fpbg, snv_lift/
+ ]
+| #p #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2 -IH1
+ elim (snv_inv_gref … H1)
+| #a #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4 -IH3 -IH2
+ elim (snv_inv_bind … H1) -H1 #HV1 #HT1
+ elim (cpr_inv_bind1 … H2) -H2 *
+ [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=8 by fqup_fpbg, snv_bind, lpr_pair/
+ | #T2 #HT12 #HXT2 #H1 #H2 destruct -HV1
+ /4 width=10 by fqup_fpbg, snv_inv_lift, lpr_pair, drop_drop/
+ ]
+| #V1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct
+ elim (snv_inv_appl … H1) -H1 #a #W1 #U1 #d0 #HV1 #HT1 #HVW1 #HTU1
+ elim (cpr_inv_appl1 … H2) -H2 *
+ [ #V2 #T2 #HV12 #HT12 #H destruct -IH4
+ lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
+ lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ #HT2
+ elim (scpds_cpr_lpr_aux … IH2 IH3 … HVW1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HVW1 -HV12 #XV #HVW2 #HXV
+ elim (scpds_cpr_lpr_aux … IH2 IH3 … HTU1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ -HTU1 -HT12 #X #HTU2 #H
+ elim (cprs_inv_abst1 … H) -H #XW #U2 #HXW #_ #H destruct -IH1 -IH3 -IH2 -L1
+ elim (cprs_conf … HXV … HXW) -W1 #W2 #HXV #HXW
+ lapply (scpds_cprs_trans … HVW2 … HXV) -XV
+ lapply (scpds_cprs_trans … (ⓛ{a}W2.U2) … HTU2 ?)
+ /2 width=7 by snv_appl, cprs_bind/
+ | #b #V2 #W10 #W20 #T10 #T20 #HV12 #HW120 #HT120 #H1 #H2 destruct
+ elim (snv_inv_bind … HT1) -HT1 #HW10 #HT10
+ elim (scpds_inv_abst1 … HTU1) -HTU1 #W30 #T30 #HW130 #_ #H destruct -T30 -d0
+ elim (snv_fwd_da … HV1) #d #HV1d
+ elim (snv_fwd_da … HW10) #d0 #HW10d
+ lapply (cprs_scpds_div … HW130 … HW10d … 1 HVW1) -W30 #HVW10
+ elim (da_scpes_aux … IH4 IH1 IH2 … HW10d … HV1d … HVW10) /2 width=1 by fqup_fpbg/
+ #_ #Hd <minus_n_O #H destruct >(plus_minus_m_m d 1) in HV1d; // -Hd #HV1d
+ lapply (scpes_cpr_lpr_aux … IH2 IH3 … HVW10 … HW120 … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HVW10 #HVW20
+ lapply (IH2 … HV1d … HV12 … HL12) /2 width=1 by fqup_fpbg/ -HV1d #HV2d
+ lapply (IH2 … HW10d … HW120 … HL12) /2 width=1 by fqup_fpbg/ -HW10d #HW20d
+ lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
+ lapply (IH1 … HW120 … HL12) /2 width=1 by fqup_fpbg/ -HW10 #HW20
+ lapply (IH1 … HT10 … HT120 … (L2.ⓛW20) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -HT10 #HT20
+ @snv_bind /2 width=1 by snv_cast_scpes/
+ @(lsubsv_snv_trans … HT20) -HT20
+ @(lsubsv_beta … (d-1)) //
+ @shnv_cast [1,2: // ] #d0 #Hd0
+ lapply (scpes_le_aux … IH4 IH1 IH2 IH3 … HW20d … HV2d … d0 … HVW20) -IH4 -IH3 -IH2 -IH1 -HW20d -HV2d -HVW20
+ /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs, le_S_S/
+ | #b #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct -IH4
+ elim (snv_inv_bind … HT1) -HT1 #HW0 #HT0
+ elim (scpds_inv_abbr_abst … HTU1) -HTU1 #X #HTU0 #HX #H destruct
+ elim (lift_inv_bind1 … HX) -HX #W3 #U3 #HW13 #_ #H destruct
+ elim (scpds_cpr_lpr_aux … IH2 IH3 … HVW1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ -HVW1 #XV #HXV0 #HXVW1
+ elim (scpds_cpr_lpr_aux … IH2 IH3 … HTU0 … HT02 (L2.ⓓW2)) /2 width=1 by fqup_fpbg, lpr_pair/ -HTU0 #X #HXT2 #H
+ elim (cprs_inv_abst1 … H) -H #W #U2 #HW3 #_ #H destruct -U3
+ 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/ -L1 #HT2
+ lapply (snv_lift … HV0 (L2.ⓓW2) (Ⓕ) … HV02) /2 width=1 by drop_drop/ -HV0 #HV2
+ elim (lift_total XV 0 1) #XW #HXVW
+ lapply (scpds_lift … HXV0 (L2.ⓓW2) (Ⓕ) … HV02 … HXVW) /2 width=1 by drop_drop/ -V0 #HXWV2
+ lapply (cprs_lift … HXVW1 (L2.ⓓW2) (Ⓕ) … HW13 … HXVW) /2 width=1 by drop_drop/ -W1 -XV #HXW3
+ elim (cprs_conf … HXW3 … HW3) -W3 #W3 #HXW3 #HW3
+ lapply (scpds_cprs_trans … HXWV2 … HXW3) -XW
+ lapply (scpds_cprs_trans … (ⓛ{a}W3.U2) … HXT2 ?) /2 width=1 by cprs_bind/ -W
+ /3 width=6 by snv_appl, snv_bind/
+ ]
+| #W1 #T1 #HG0 #HL0 #HT0 #H1 #X #H2 #L2 #HL12 destruct -IH4
+ elim (snv_inv_cast … H1) -H1 #U1 #HW1 #HT1 #HWU1 #HTU1
+ elim (cpr_inv_cast1 … H2) -H2
+ [ * #W2 #T2 #HW12 #HT12 #H destruct
+ elim (snv_fwd_da … HW1) #d #HW1d
+ lapply (scpds_div … HWU1 … HTU1) -U1 -d #HWT1
+ lapply (scpes_cpr_lpr_aux … IH2 IH3 … HWT1 … HW12 … HT12 … HL12) /2 width=1 by fqup_fpbg/
+ lapply (IH1 … HW12 … HL12) /2 width=1 by fqup_fpbg/
+ lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ -L1
+ /2 width=1 by snv_cast_scpes/
+ | #H -IH3 -IH2 -HW1 -U1
+ lapply (IH1 … H … HL12) /2 width=1 by fqup_fpbg/
+ ]
+]
+qed-.
projects / helm.git / blobdiff