(**************************************************************************)
include "basic_2/unwind/sstas_sstas.ma".
-include "basic_2/computation/ygt.ma".
include "basic_2/equivalence/cpcs_ltpr.ma".
include "basic_2/dynamic/snv_ltpss_dx.ma".
include "basic_2/dynamic/snv_sstas.ma".
+include "basic_2/dynamic/ygt.ma".
(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
λh,g,L1,T1. ⦃h, L1⦄ ⊩ T1 :[g] →
∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l + 1] U1 → ⦃h, L1⦄ ⊩ U1 :[g].
+(* Properties for the preservation results **********************************)
+
+definition IH_snv_lsubsv: ∀h:sh. sd h → relation2 lenv term ≝
+ λh,g,L2,T. ⦃h, L2⦄ ⊩ T :[g] →
+ ∀L1. h ⊢ L1 ⊩:⊑[g] L2 → ⦃h, L1⦄ ⊩ T :[g].
+
fact snv_ltpr_cpr_aux: ∀h,g,L1,T1. IH_snv_ltpr_tpr h g L1 T1 →
⦃h, L1⦄ ⊩ T1 :[g] →
∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡ T2 → ⦃h, L2⦄ ⊩ T2 :[g].