-inductive aaa: lenv → term → predicate aarity ≝
-| aaa_sort: ∀L,k. aaa L (⋆k) ⓪
-| aaa_lref: ∀I,L,K,V,B,i. ⇩[0, i] L ≡ K. ⓑ{I} V → aaa K V B → aaa L (#i) B
-| aaa_abbr: ∀a,L,V,T,B,A.
- aaa L V B → aaa (L. ⓓV) T A → aaa L (ⓓ{a}V. T) A
-| aaa_abst: ∀a,L,V,T,B,A.
- aaa L V B → aaa (L. ⓛV) T A → aaa L (ⓛ{a}V. T) (②B. A)
-| aaa_appl: ∀L,V,T,B,A. aaa L V B → aaa L T (②B. A) → aaa L (ⓐV. T) A
-| aaa_cast: ∀L,V,T,A. aaa L V A → aaa L T A → aaa L (ⓝV. T) A
+(* activate genv *)
+inductive aaa: relation4 genv lenv term aarity ≝
+| aaa_sort: ∀G,L,k. aaa G L (⋆k) (⓪)
+| aaa_lref: ∀I,G,L,K,V,B,i. ⇩[i] L ≡ K. ⓑ{I}V → aaa G K V B → aaa G L (#i) B
+| aaa_abbr: ∀a,G,L,V,T,B,A.
+ aaa G L V B → aaa G (L.ⓓV) T A → aaa G L (ⓓ{a}V.T) A
+| aaa_abst: ∀a,G,L,V,T,B,A.
+ aaa G L V B → aaa G (L.ⓛV) T A → aaa G L (ⓛ{a}V.T) (②B.A)
+| aaa_appl: ∀G,L,V,T,B,A. aaa G L V B → aaa G L T (②B.A) → aaa G L (ⓐV.T) A
+| aaa_cast: ∀G,L,V,T,A. aaa G L V A → aaa G L T A → aaa G L (ⓝV.T) A