case zero =>
  intro n₂
  show 0 ≃ n₂ → 0 + m ≃ n₂ + m
  apply cases_on (motive := λ y => 0 ≃ y → 0 + m ≃ y + m)
  case zero =>
    intro (_ : 0 ≃ (0 : ℕ))
    show 0 + m ≃ 0 + m
    exact Rel.refl
  case step =>
    intro n₂ (_ : 0 ≃ step n₂)
    exact absurd (Rel.symm ‹0 ≃ step n₂›) step_neqv_zero
ℕ : Type
inst✝² : Core ℕ
inst✝¹ : Induction ℕ
inst✝ : Addition ℕ
n₁ n₂ m : ℕ
⊢ ∀ (y : ℕ), 0 ≃ y → 0 + m ≃ y + m
no goals