have := ArithPart₁.map (fun v x => isEqNat x (v.get i)) (this.of_eq $ by simp) (ArithPart₁.rfindPos hF)
n : ℕ
p : Vector ℕ n → ℕ → ℕ
hp : Arith₁ fun v => p v.tail v.head
i : Fin n
F : Vector ℕ (n + 1) → ℕ := fun v => (p v.tail v.head).inv.or ((v.get i.succ).isLeNat v.head)
hF : Arith₁ F
this : Arith₁ fun v => v.head.isEqNat (v.get i.succ)
⊢ Arith₁ fun v => (v.get i).ball (p v)
n : ℕ
p : Vector ℕ n → ℕ → ℕ
hp : Arith₁ fun v => p v.tail v.head
i : Fin n
F : Vector ℕ (n + 1) → ℕ := fun v => (p v.tail v.head).inv.or ((v.get i.succ).isLeNat v.head)
hF : Arith₁ F
this✝ : Arith₁ fun v => v.head.isEqNat (v.get i.succ)
this :
  ArithPart₁ fun v =>
    Part.map ((fun v x => x.isEqNat (v.get i)) v) (rfind fun n_1 => Part.some (decide (0 < F (n_1 ::ᵥ v))))
⊢ Arith₁ fun v => (v.get i).ball (p v)