-(* Note: this is not transitive *)
-inductive lsubv (a) (h) (G): relation lenv ≝
-| lsubv_atom: lsubv a h G (⋆) (⋆)
-| lsubv_bind: ∀I,L1,L2. lsubv a h G L1 L2 → lsubv a h G (L1.ⓘ{I}) (L2.ⓘ{I})
-| lsubv_beta: ∀L1,L2,W,V. ⦃G, L1⦄ ⊢ ⓝW.V ![a,h] → ⦃G, L2⦄ ⊢ W ![a,h] →
- lsubv a h G L1 L2 → lsubv a h G (L1.ⓓⓝW.V) (L2.ⓛW)
+inductive lsubv (h) (a) (G): relation lenv ≝
+| lsubv_atom: lsubv h a G (⋆) (⋆)
+| lsubv_bind: ∀I,L1,L2. lsubv h a G L1 L2 → lsubv h a G (L1.ⓘ{I}) (L2.ⓘ{I})
+| lsubv_beta: ∀L1,L2,W,V. ⦃G,L1⦄ ⊢ ⓝW.V ![h,a] →
+ lsubv h a G L1 L2 → lsubv h a G (L1.ⓓⓝW.V) (L2.ⓛW)