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/computation/cpds_cpds.ma".
16 include "basic_2/dynamic/snv_aaa.ma".
17 include "basic_2/dynamic/lsubsv_cpds.ma".
18 include "basic_2/dynamic/lsubsv_cpcs.ma".
20 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
22 (* Properties concerning stratified native validity *************************)
24 lemma lsubsv_snv_trans: ∀h,g,G,L2,T. ⦃G, L2⦄ ⊢ T ¡[h, g] →
25 ∀L1. G ⊢ L1 ¡⫃[h, g] L2 → ⦃G, L1⦄ ⊢ T ¡[h, g].
26 #h #g #G #L2 #T #H elim H -G -L2 -T //
27 [ #I #G #L2 #K2 #V #i #HLK2 #_ #IHV #L1 #HL12
28 elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
29 elim (lsubsv_inv_pair2 … H) -H * #K1
30 [ #HK12 #H destruct /3 width=5 by snv_lref/
31 | #W #l #H1V #H1W #HWV #_ #HWl #_ #_ #H1 #H2 destruct -IHV
32 /3 width=10 by snv_scast, snv_lref/
34 | #a #I #G #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 destruct
35 /4 width=1 by snv_bind, lsubsv_pair/
36 | #a #G #L2 #V #W #W0 #T #U #l #_ #_ #HVl #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
37 lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
38 elim (lsubsv_ssta_trans … HVW … HVl … HL12) -HVW #W1 #HVW1 #HW1
39 lapply (cpcs_cprs_strap1 … HW1 … HW0) -W #HW10
40 lapply (lsubd_da_trans … HVl L1 ?) -HVl /2 width=1 by lsubsv_fwd_lsubd/ #HVl
41 elim (lsubsv_cpds_trans … HTU … HL12) -HTU #X #HTU #H
42 elim (cprs_inv_abst1 … H) -H #W #U2 #HW0 #_ #H destruct
43 lapply (cpcs_cprs_strap1 … HW10 … HW0) -W0 #H
44 elim (cpcs_inv_cprs … H) -H #W0 #HW10 #HW0
45 /4 width=11 by snv_appl, cpds_cprs_trans, cprs_bind/
46 | #G #L2 #W #T #U #l #_ #_ #HTl #HTU #HUW #IHW #IHT #L1 #HL12
47 lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
48 elim (lsubsv_ssta_trans … HTU … HTl … HL12) -HTU #U0 #HTU0 #HU0
49 lapply (lsubd_da_trans … HTl L1 ?) -HTl
50 /4 width=5 by lsubsv_fwd_lsubd, snv_cast, cpcs_trans/