have ⟨(d : ℕ), (_ : Positive d), (_ : n₂ ≃ n₁ + d)⟩ :=
  lt_defn_add.mp ‹n₁ < n₂›
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n₁ n₂ m : ℕ
x✝¹ : Positive m
x✝ : n₁ < n₂
⊢ n₁ * m < n₂ * m
ℕ : Type
inst✝⁵ : Core ℕ
inst✝⁴ : Induction ℕ
inst✝³ : Addition ℕ
inst✝² : Sign ℕ
inst✝¹ : Order ℕ
inst✝ : Multiplication ℕ
n₁ n₂ m : ℕ
x✝¹ : Positive m
x✝ : n₁ < n₂
d : ℕ
left✝ : Positive d
right✝ : n₂ ≃ n₁ + d
⊢ n₁ * m < n₂ * m