1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/rt_computation/cpms_fpbg.ma".
16 include "basic_2/rt_computation/cprs_cprs.ma".
17 include "basic_2/rt_computation/lprs_cpms.ma".
18 include "basic_2/dynamic/cnv_drops.ma".
20 include "basic_2/dynamic/snv_aaa.ma".
22 include "basic_2/dynamic/cnv_etc.ma".
24 include "basic_2/dynamic/lsubsv_snv.ma".
26 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
28 (* Properties with context-free parallel reduction for local environments *****)
30 fact cnv_cpm_trans_lpr_aux (a) (h) (o): a = Ⓕ →
32 (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpms_conf_lpr a h G1 L1 T1) →
33 (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, o] ⦃G1, L1, T1⦄ → IH_cnv_cpm_trans_lpr a h G1 L1 T1) →
34 ∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_cnv_cpm_trans_lpr a h G1 L1 T1.
35 #a #h #o #Ha #G0 #L0 #T0 (* #IH4 #IH3 *) #IH2 #IH1 #G1 #L1 * * [|||| * ]
36 [ #s #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #_ destruct (* -IH4 -IH3 *) -IH2 -IH1 -H1
37 elim (cpm_inv_sort1 … H2) -H2 * #H1 #H2 destruct //
38 | #i #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct (* -IH4 -IH3 *) -IH2
39 elim (cnv_inv_lref_drops … H1) -H1 #I #K1 #V1 #HLK1 #HV1
40 elim (lpr_drops_conf … HLK1 … HL12) -HL12 // #Y #H #HLK2
41 elim (lpr_inv_pair_sn … H) -H #K2 #V2 #HK12 #HV12 #H destruct
42 lapply (fqup_lref (Ⓣ) … G1 … HLK1) #HKL
43 elim (cpm_inv_lref1_drops … H2) -H2 *
44 [ #H1 #H2 destruct -HLK1 /4 width=7 by fqup_fpbg, cnv_lref_drops/
45 | #K0 #V0 #W0 #H #HVW0 #W0 -HV12
46 lapply (drops_mono … H … HLK1) -HLK1 -H #H destruct
47 lapply (drops_isuni_fwd_drop2 … HLK2) -HLK2 /4 width=7 by fqup_fpbg, cnv_lifts/
48 | #n #K0 #V0 #W0 #H #HVW0 #W0 #H destruct -HV12
49 lapply (drops_mono … H … HLK1) -HLK1 -H #H destruct
50 lapply (drops_isuni_fwd_drop2 … HLK2) -HLK2 /4 width=7 by fqup_fpbg, cnv_lifts/
52 | #l #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct (* -IH4 -IH3 *) -IH2 -IH1
53 elim (cnv_inv_gref … H1)
54 | #p #I #V1 #T1 #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct (* -IH4 -IH3 *) -IH2
55 elim (cnv_inv_bind … H1) -H1 #HV1 #HT1
56 elim (cpm_inv_bind1 … H2) -H2 *
57 [ #V2 #T2 #HV12 #HT12 #H destruct /4 width=9 by fqup_fpbg, cnv_bind, lpr_pair/
58 | #T2 #HT12 #HXT2 #H1 #H2 destruct -HV1
59 /4 width=11 by fqup_fpbg, cnv_inv_lifts, lpr_pair, drops_refl, drops_drop/
61 | #V1 #T1 #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct
62 elim (cnv_inv_appl … H1) -H1 #n #p #W1 #U1 #Hn #HV1 #HT1 #HVW1 #HTU1
63 elim (cpm_inv_appl1 … H2) -H2 *
64 [ #V2 #T2 #HV12 #HT12 #H destruct (* -IH4 *)
65 lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
66 lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ #HT2
67 elim (IH2 … HVW1 … V2 … L2 … L2) [|*: /2 width=2 by fqup_fpbg, cpm_cpms/ ] -HVW1 -HV12
68 <minus_n_O <minus_O_n #XW1 #HXW1 #HXV2
69 elim (IH2 … HTU1 … T2 … L2 … L2) [|*: /2 width=2 by fqup_fpbg, cpm_cpms/ ] -HTU1 -HT12
70 #X #H #HTU2 (* -IH3 *) -IH2 -IH1 -L1 -V1 -T1
71 elim (cpms_inv_abst_sn … H) -H #W2 #U2 #HW12 #_ #H destruct
72 elim (cprs_conf … HXW1 … HW12) -W1 #W1 #HXW1 #HW21
73 lapply (cpms_trans … HXV2 … HXW1) -XW1 <plus_n_O #HV2W1
74 lapply (cpms_trans … HTU2 … (ⓛ{p}W1.U2) ?)
75 [3:|*: /2 width=2 by cpms_bind/ ] -W2 <plus_n_O #HTU2
76 @(cnv_appl … HV2W1 HTU2) // #H destruct
77 | #q #V2 #W10 #W20 #T10 #T20 #HV12 #HW120 #HT120 #H1 #H2 destruct
78 elim (cnv_inv_bind … HT1) -HT1 #HW10 #HT10
79 elim (cpms_inv_abst_sn … HTU1) -HTU1 #W30 #T30 #HW130 #_ #H destruct -T30
80 lapply (IH1 … HV12 … HL12) /2 width=1 by fqup_fpbg/ #HV2
81 lapply (IH1 … HW120 … HL12) /2 width=1 by fqup_fpbg/ #HW20
82 lapply (IH1 … HT10 … HT120 … (L2.ⓛW20) ?) /2 width=1 by fqup_fpbg, lpr_pair/ -HT10 -HT120 #HT20
83 elim (IH2 … HVW1 … V2 … L2 … L2) [|*: /2 width=2 by fqup_fpbg, cpm_cpms/ ] -HVW1 -HV12
84 <minus_n_O <minus_O_n #XW1 #HXW1 #HXV2
85 elim (IH2 … HW130 … W20 … L2 … L2) [|*: /2 width=2 by fqup_fpbg, cpm_cpms/ ] -HW130 -HW120
86 <minus_n_O #XW30 #HXW30 #HW230
87 elim (cprs_conf … HXW1 … HXW30) -W30 #W30 #HXW1 #HXW30
88 lapply (cpms_trans … HXV2 … HXW1) -XW1 <plus_n_O #HV2W30
89 lapply (cprs_trans … HW230 … HXW30) -XW30 #HW230
90 @cnv_bind [ /2 width=3 by cnv_cast/ ]
92 @(lsubsv_snv_trans … HT20) -HT20
93 @(lsubsv_beta … (d-1)) //
94 @shnv_cast [1,2: // ] #d0 #Hd0
95 lapply (scpes_le_aux … IH4 IH1 IH2 IH3 … HW20d … HV2d … d0 … HVW20) -IH4 -IH3 -IH2 -IH1 -HW20d -HV2d -HVW20
96 /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, cpr_lpr_fpbs, le_S_S/
98 | #q #V0 #V2 #W0 #W2 #T0 #T2 #HV10 #HV02 #HW02 #HT02 #H1 #H2 destruct (* -IH4 *)
99 elim (cnv_inv_bind … HT1) -HT1 #HW0 #HT0
100 elim (cpms_inv_abbr_abst … HTU1) -HTU1 #X #HTU0 #HX #H destruct
101 elim (lifts_inv_bind1 … HX) -HX #W3 #U3 #HW13 #_ #H destruct
102 lapply (IH1 … HW02 … HL12) /2 width=1 by fqup_fpbg/ #HW2
103 lapply (IH1 … HV10 … HL12) /2 width=1 by fqup_fpbg/ #HV0
104 lapply (IH1 … HT02 (L2.ⓓW2) ?) /2 width=1 by fqup_fpbg, lpr_pair/ #HT2
105 elim (IH2 … HVW1 … V0 … L2 … L2) [|*: /2 width=2 by fqup_fpbg, cpm_cpms/ ] -HVW1 -HV10
106 <minus_n_O <minus_O_n #XW1 #HXW1 #HXV0
107 elim (IH2 … HTU0 … T2 … (L2.ⓓW2) … (L2.ⓓW2)) [|*: /2 width=2 by fqup_fpbg, cpm_cpms, lpr_pair/ ] -HT02 -HTU0 -HW02
108 #X #H #HTU2 -IH2 -IH1
109 elim (cpms_inv_abst_sn … H) -H #W #U2 #HW3 #_ #H destruct -U3
110 lapply (cnv_lifts … HV0 (Ⓣ) … (L2.ⓓW2) … HV02) /3 width=1 by drops_refl, drops_drop/ -HV0 #HV2
111 elim (cpms_lifts_sn … HXV0 (Ⓣ) … (L2.ⓓW2) … HV02) /3 width=1 by drops_refl, drops_drop/ -V0 #XW2 #HXW12 #HXVW2
112 lapply (cpms_lifts_bi … HXW1 (Ⓣ) … (L2.ⓓW2) … HW13 … HXW12) /3 width=1 by drops_refl, drops_drop/ -W1 -XW1 #HXW32
113 elim (cprs_conf … HXW32 … HW3) -W3 #W3 #HXW23 #HW3
114 lapply (cpms_trans … HXVW2 … HXW23) -XW2 <plus_n_O #H1
115 lapply (cpms_trans … HTU2 ? (ⓛ{p}W3.U2) ?) [3:|*:/2 width=2 by cpms_bind/ ] -W #H2
116 @cnv_bind // @(cnv_appl … H1 H2) // #H destruct
118 | #W1 #T1 #HG0 #HL0 #HT0 #H1 #x #X #H2 #L2 #HL12 destruct (* -IH4 *)
119 elim (cnv_inv_cast … H1) -H1 #U1 #HW1 #HT1 #HWU1 #HTU1
120 elim (cpm_inv_cast1 … H2) -H2
121 [ * #W2 #T2 #HW12 #HT12 #H destruct
122 lapply (IH1 … HW12 … HL12) /2 width=1 by fqup_fpbg/ #HW2
123 lapply (IH1 … HT12 … HL12) /2 width=1 by fqup_fpbg/ #HT2
124 lapply (cnv_cpms_trans_lpr_aux … IH1 … HTU1 L1 ?) /2 width=1 by fqup_fpbg/ #HU1
125 elim (IH2 … HWU1 … W2 … L1 … HL12) [|*: /2 width=2 by fqup_fpbg, cpm_cpms/ ] -HW12
126 <minus_n_O <minus_O_n #XW1 #HXUW1 #HXW21
127 elim (IH2 … HTU1 … T2 … L1 … HL12) [|*: /2 width=2 by fqup_fpbg, cpm_cpms/ ] -HTU1 -HT12
129 elim (IH2 … HXUW1 … HXUT1 … HL12 … HL12) [|*: /2 width=4 by fqup_cpms_fwd_fpbg/ ] -HXUW1 -HXUT1 -HWU1
130 >eq_minus_O // #W0 #H1 #H2
131 lapply (cprs_trans … HXW21 … H1) -XW1 #H1
132 lapply (cpms_trans … HXT21 … H2) -XT1 <arith_l #H2
133 /2 width=3 by cnv_cast/
134 | #HX (* -IH3 *) -IH2 -HW1 -U1
135 lapply (IH1 … HX … HL12) /2 width=1 by fqup_fpbg/
136 | * #n #HX #H destruct -IH2 -HT1 -U1
137 lapply (IH1 … HX … HL12) /2 width=1 by fqup_fpbg/