case mpr =>
  intro (_ : a ≃ 0 ∨ b ≃ 0)
  show a * b ≃ 0
  match ‹a ≃ 0 ∨ b ≃ 0› with
  | Or.inl (_ : a ≃ 0) => calc
    a * b ≃ _ := AA.substL ‹a ≃ 0›
    0 * b ≃ _ := AA.absorbL
    0     ≃ _ := Rel.refl
  | Or.inr (_ : b ≃ 0) => calc
    a * b ≃ _ := AA.substR ‹b ≃ 0›
    a * 0 ≃ _ := AA.absorbR
    0     ≃ _ := Rel.refl
ℕ : Type
inst✝⁵ : Natural ℕ
ℤ : Type
inst✝⁴ : Core ℤ
inst✝³ : Addition ℤ
inst✝² : Multiplication ℤ
inst✝¹ : Negation ℤ
inst✝ : Sign ℤ
a b : ℤ
⊢ a ≃ 0 ∨ b ≃ 0 → a * b ≃ 0
no goals