simp only [shiftList]
case h
D : Type
V : VarAssignment D
hd : String
tl : List String
ih : V ∘ Var.openList 0 (List.map free_ tl) = shiftList D V (List.map (V ∘ free_) tl)
v : Var
⊢ V (Var.openList 0 (free_ hd :: List.map free_ tl) v) = shiftList D V (V (free_ hd) :: List.map (V ∘ free_) tl) v
case h
D : Type
V : VarAssignment D
hd : String
tl : List String
ih : V ∘ Var.openList 0 (List.map free_ tl) = shiftList D V (List.map (V ∘ free_) tl)
v : Var
⊢ V (Var.openList 0 (free_ hd :: List.map free_ tl) v) =
    shift D (shiftList D V (List.map (V ∘ free_) tl)) (V (free_ hd)) v