have : n₂ * m ≃ n₁ * m + d * m := calc
  n₂ * m         ≃ _ := AA.substL ‹n₂ ≃ n₁ + d›
  (n₁ + d) * m   ≃ _ := AA.distribR
  n₁ * m + d * m ≃ _ := Rel.refl
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
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
this : n₂ * m ≃ n₁ * m + d * m
⊢ n₁ * m < n₂ * m