. exact permuted_map_invertible p
case left
α : Type
n first last : Nat
arr arr' : Vec α n
p : permuted n first last arr arr'
⊢ invertible p.to_map

case right
α : Type
n first last : Nat
arr arr' : Vec α n
p : permuted n first last arr arr'
⊢ ∀ (i : Fin n), arr[i] = arr'[p.to_map i]
case right
α : Type
n first last : Nat
arr arr' : Vec α n
p : permuted n first last arr arr'
⊢ ∀ (i : Fin n), arr[i] = arr'[p.to_map i]