apply Exists.elim ih
hd : Var
tl : List Var
h1_left : Var.lc_at 0 hd
h1_right : ∀ a ∈ tl, Var.lc_at 0 a
ih : ∃ xs, tl = List.map free_ xs
⊢ ∃ xs, hd :: tl = List.map free_ xs
hd : Var
tl : List Var
h1_left : Var.lc_at 0 hd
h1_right : ∀ a ∈ tl, Var.lc_at 0 a
ih : ∃ xs, tl = List.map free_ xs
⊢ ∀ (a : List String), tl = List.map free_ a → ∃ xs, hd :: tl = List.map free_ xs