--- /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_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".
+include "basic_2/dynamic/cnv_etc.ma".
+include "basic_2/dynamic/lsubv_cnv.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Properties with context-free parallel reduction for local environments *****)
+
+fact cnv_cpm_trans_lpr_aux (a) (h) (o): a = Ⓕ →
+ ∀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 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_trans_lpr a h G1 L1 T1.
+#a #h #o #Ha #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 //
+| #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 (lpr_inv_pair_sn … H) -H #K2 #V2 #HK12 #HV12 #H destruct
+ lapply (fqup_lref (Ⓣ) … G1 … HLK1) #HKL
+ elim (cpm_inv_lref1_drops … H2) -H2 *
+ [ #H1 #H2 destruct -HLK1 /4 width=7 by fqup_fpbg, cnv_lref_drops/
+ | #K0 #V0 #W0 #H #HVW0 #W0 -HV12
+ lapply (drops_mono … H … HLK1) -HLK1 -H #H destruct
+ lapply (drops_isuni_fwd_drop2 … HLK2) -HLK2 /4 width=7 by fqup_fpbg, cnv_lifts/
+ | #n #K0 #V0 #W0 #H #HVW0 #W0 #H destruct -HV12
+ lapply (drops_mono … H … HLK1) -HLK1 -H #H destruct
+ lapply (drops_isuni_fwd_drop2 … HLK2) -HLK2 /4 width=7 by fqup_fpbg, cnv_lifts/
+ ]
+| #l #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct -IH2 -IH1
+ elim (cnv_inv_gref … H1)
+| #p #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct -IH2
+ 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/
+ ]
+| #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
+ elim (cpm_inv_appl1 … H2) -H2 *
+ [ #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
+ <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
+ #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 (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
+ @(cnv_appl … HV2W1 HTU2) // #H destruct
+ | #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
+ 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
+ <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
+ <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 (cprs_trans … HW230 … HXW30) -XW30 #HW230
+ /5 width=4 by lsubv_cnv_trans, lsubv_beta, cnv_cast, cnv_bind/
+ | #q #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct
+ elim (cnv_inv_bind … HT1) -HT1 #HW0 #HT0
+ elim (cpms_inv_abbr_abst … HTU1) -HTU1 #X #HTU0 #HX #H destruct
+ elim (lifts_inv_bind1 … HX) -HX #W3 #U3 #HW13 #_ #H destruct
+ 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
+ <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
+ #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
+ elim (cpms_lifts_sn … HXV0 (Ⓣ) … (L2.ⓓW2) … HV02) /3 width=1 by drops_refl, drops_drop/ -V0 #XW2 #HXW12 #HXVW2
+ lapply (cpms_lifts_bi … HXW1 (Ⓣ) … (L2.ⓓW2) … HW13 … HXW12) /3 width=1 by drops_refl, drops_drop/ -W1 -XW1 #HXW32
+ 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
+ @cnv_bind // @(cnv_appl … H1 H2) // #H destruct
+ ]
+| #W1 #T1 #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct
+ elim (cnv_inv_cast … H1) -H1 #U1 #HW1 #HT1 #HWU1 #HTU1
+ elim (cpm_inv_cast1 … H2) -H2
+ [ * #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
+ <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
+ #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
+ /2 width=3 by cnv_cast/
+ | #HX -IH2 -HW1 -U1
+ lapply (IH1 … HX … HL12) /2 width=1 by fqup_fpbg/
+ | * #n #HX #H destruct -IH2 -HT1 -U1
+ lapply (IH1 … HX … HL12) /2 width=1 by fqup_fpbg/
+ ]
+]
+qed-.
projects / helm.git / blobdiff