have tri : AA.OneOfThree (n < m) (n ≃ m) (n > m) :=
  (trichotomy n m).atLeastOne
ℕ : Type
inst✝⁴ : Core ℕ
inst✝³ : Induction ℕ
inst✝² : Addition ℕ
inst✝¹ : Sign ℕ
order_inst : Order ℕ
inst✝ : Compare ℕ
n m k : ℕ
⊢ compare n m = compare (n + k) (m + k)
ℕ : Type
inst✝⁴ : Core ℕ
inst✝³ : Induction ℕ
inst✝² : Addition ℕ
inst✝¹ : Sign ℕ
order_inst : Order ℕ
inst✝ : Compare ℕ
n m k : ℕ
tri : AA.OneOfThree (n < m) (n ≃ m) (n > m)
⊢ compare n m = compare (n + k) (m + k)