intro e hzero hsucc x
n : ℕ
μ : Type v
e : Fin n → ℕ
ε : μ → ℕ
p : Semiformula ℒₒᵣ ℕ 1
⊢ ∀ (ε : ℕ → ℕ),
    (Semiformula.Eval (standardModel ℕ) ![0] ε) p →
      (∀ (x : ℕ), (Semiformula.Eval (standardModel ℕ) ![x] ε) p → (Semiformula.Eval (standardModel ℕ) ![x + 1] ε) p) →
        ∀ (x : ℕ), (Semiformula.Eval (standardModel ℕ) ![x] ε) p
n : ℕ
μ : Type v
e✝ : Fin n → ℕ
ε : μ → ℕ
p : Semiformula ℒₒᵣ ℕ 1
e : ℕ → ℕ
hzero : (Semiformula.Eval (standardModel ℕ) ![0] e) p
hsucc : ∀ (x : ℕ), (Semiformula.Eval (standardModel ℕ) ![x] e) p → (Semiformula.Eval (standardModel ℕ) ![x + 1] e) p
x : ℕ
⊢ (Semiformula.Eval (standardModel ℕ) ![x] e) p