induction F
x : ℕ
ρ : Formula
F : List Formula
nonOcc : x ∉ voc F
⊢ List.map (repl_in_F x ρ) F = F
case nil
x : ℕ
ρ : Formula
nonOcc : x ∉ voc []
⊢ List.map (repl_in_F x ρ) [] = []

case cons
x : ℕ
ρ head✝ : Formula
tail✝ : List Formula
tail_ih✝ : x ∉ voc tail✝ → List.map (repl_in_F x ρ) tail✝ = tail✝
nonOcc : x ∉ voc (head✝ :: tail✝)
⊢ List.map (repl_in_F x ρ) (head✝ :: tail✝) = head✝ :: tail✝