(* *)
(**************************************************************************)
-include "basic_2/dynamic/lsubsv_ldrop.ma".
-(*
-include "basic_2/dynamic/lsubsv_ssta.ma".
-include "basic_2/dynamic/lsubsv_cpcs.ma".
-*)
+include "basic_2/dynamic/lsubsv_scpds.ma".
+
(* LOCAL ENVIRONMENT REFINEMENT FOR STRATIFIED NATIVE VALIDITY **************)
(* Properties concerning stratified native validity *************************)
-(*
-axiom lsubsv_xprs_trans: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
- ∀T1,T2. ⦃h, L2⦄ ⊢ T1 •➡*[g] T2 → ⦃h, L1⦄ ⊢ T1 •➡*[g] T2.
-/3 width=3 by lsubsv_fwd_lsubss, lsubss_xprs_trans/ qed-.
-*)
-axiom lsubsv_snv_trans: ∀h,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
- ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
-(*
-#h #g #L2 #T #H elim H -L2 -T //
-[ #I2 #L2 #K2 #V2 #i #HLK2 #_ #IHV2 #L1 #HL12
- elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
- elim (lsubsv_inv_pair2 … H) -H * #K1 [ | -IHV2 ]
- [ #HK12 #H destruct /3 width=5/
- | #V1 #l #HV1 #_ #_ #_ #H destruct /2 width=5/
+lemma lsubsv_snv_trans: ∀h,o,G,L2,T. ⦃G, L2⦄ ⊢ T ¡[h, o] →
+ ∀L1. G ⊢ L1 ⫃¡[h, o] L2 → ⦃G, L1⦄ ⊢ T ¡[h, o].
+#h #o #G #L2 #T #H elim H -G -L2 -T //
+[ #I #G #L2 #K2 #V #i #HLK2 #_ #IHV #L1 #HL12
+ elim (lsubsv_drop_O1_trans … HL12 … HLK2) -L2 #X #H #HLK1
+ elim (lsubsv_inv_pair2 … H) -H * #K1
+ [ #HK12 #H destruct /3 width=5 by snv_lref/
+ | #W #d #HVW #_ #_ #_ #_ #H1 #H2 destruct -IHV
+ /3 width=6 by shnv_inv_snv, snv_lref/
]
-| #a #I #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 /4 width=1/
-| #a #L2 #V #W #W0 #T #U #l #_ #_ #HVW #HW0 #HTU #IHV #IHT #L1 #HL12
- lapply (IHV … HL12) -IHV #HV
- lapply (IHT … HL12) -IHT #HT
- lapply (lsubsv_ssta_trans … HVW … HL12) -HVW #HVW
- lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
- lapply (lsubsv_xprs_trans … HL12 … HTU) -HL12 -HTU /2 width=8/
-| #L2 #W #T #U #l #_ #_ #HTU #HWU #IHW #IHT #L1 #HL12
- lapply (IHW … HL12) -IHW #HW
- lapply (IHT … HL12) -IHT #HT
- lapply (lsubsv_ssta_trans … HTU … HL12) -HTU #HTU
- lapply (lsubsv_cpcs_trans … HL12 … HWU) -HL12 -HWU /2 width=4/
+| #a #I #G #L2 #V #T #_ #_ #IHV #IHT #L1 #HL12 destruct
+ /4 width=1 by snv_bind, lsubsv_pair/
+| #a #G #L2 #V #W0 #T #U0 #d #_ #_ #HVW0 #HTU0 #IHV #IHT #L1 #HL12
+ elim (lsubsv_scpds_trans … HVW0 … HL12) -HVW0 #V0 #HV0 #HWV0
+ elim (lsubsv_scpds_trans … HTU0 … HL12) -HTU0 #X #HT0 #H
+ elim (cprs_inv_abst1 … H) -H #W #T0 #HW0 #_ #H destruct
+ elim (cprs_conf … HWV0 … HW0) -W0
+ /4 width=10 by snv_appl, scpds_cprs_trans, cprs_bind/
+| #G #L2 #U #T #U0 #_ #_ #HU0 #HTU0 #IHU #IHT #L1 #HL12
+ elim (lsubsv_scpds_trans … HTU0 … HL12) -HTU0 #X0 #HTX0 #H1
+ elim (lsubsv_scpds_trans … HU0 … HL12) -HU0 #X #HUX #H2
+ elim (cprs_conf … H1 … H2) -U0 /3 width=5 by snv_cast, scpds_cprs_trans/
]
qed-.
-*)