induction vs
vs : List Var
h1 : ∀ v ∈ vs, Var.lc_at 0 v
⊢ ∃ xs, vs = List.map free_ xs
case nil
h1 : ∀ v ∈ [], Var.lc_at 0 v
⊢ ∃ xs, [] = List.map free_ xs

case cons
head✝ : Var
tail✝ : List Var
tail_ih✝ : (∀ v ∈ tail✝, Var.lc_at 0 v) → ∃ xs, tail✝ = List.map free_ xs
h1 : ∀ v ∈ head✝ :: tail✝, Var.lc_at 0 v
⊢ ∃ xs, head✝ :: tail✝ = List.map free_ xs