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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 *)
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15 include "basic_2/dynamic/lsubsv_ldrop.ma".
16 include "basic_2/dynamic/lsubsv_ssta.ma".
17 include "basic_2/dynamic/lsubsv_cpcs.ma".
19 (* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
21 (* Properties concerning stratified native validity *************************)
23 axiom lsubsv_xprs_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
24 ∀T1,T2. ⦃h, L2⦄ ⊢ T1 •➡*[g] T2 → ⦃h, L1⦄ ⊢ T1 •➡*[g] T2.
26 /3 width=3 by lsubsv_fwd_lsubss, lsubss_xprs_trans/ qed-.
28 axiom lsubsv_snv_trans: ∀h,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
29 ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
31 #h #g #L2 #T #H elim H -L2 -T //
32 [ #I2 #L2 #K2 #V2 #i #HLK2 #_ #IHV2 #L1 #HL12
33 elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
34 elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -IHV2 ]
35 [ #HK12 #H destruct /3 width=5/
36 | #V1 #l #HV1 #_ #_ #_ #H destruct /2 width=5/
38 | #a #I #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 /4 width=1/
39 | #a #L2 #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
40 lapply (IHV … HL12) -IHV #HV
41 lapply (IHT … HL12) -IHT #HT
42 lapply (lsubsv_ssta_trans … HVW … HL12) -HVW #HVW
43 lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
44 lapply (lsubsv_xprs_trans … HL12 … HTU) -HL12 -HTU /2 width=8/
45 | #L2 #W #T #U #l #_ #_ #HTU #HWU #IHW #IHT #L1 #HL12
46 lapply (IHW … HL12) -IHW #HW
47 lapply (IHT … HL12) -IHT #HT
48 lapply (lsubsv_ssta_trans … HTU … HL12) -HTU #HTU
49 lapply (lsubsv_cpcs_trans … HL12 … HWU) -HL12 -HWU /2 width=4/