match this with
| AA.OneOfThree.first (_ : p < q) =>
  have : p < q ∨ p ≃ q := Or.inl ‹p < q›
  have : p ≤ q := le_cases.mpr this
  have : p ≤ q ∨ q ≤ p := Or.inl this
  exact this
| AA.OneOfThree.second (_ : p ≃ q) =>
  have : p < q ∨ p ≃ q := Or.inr ‹p ≃ q›
  have : p ≤ q := le_cases.mpr this
  have : p ≤ q ∨ q ≤ p := Or.inl this
  exact this
| AA.OneOfThree.third (_ : p > q) =>
  have : q < p ∨ q ≃ p := Or.inl ‹q < p›
  have : q ≤ p := le_cases.mpr this
  have : p ≤ q ∨ q ≤ p := Or.inr this
  exact this
ℕ ℤ ℚ : Type
inst✝¹⁰ : Natural ℕ
inst✝⁹ : Integer ℤ
inst✝⁸ : Core ℚ
inst✝⁷ : Addition ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Negation ℚ
inst✝⁴ : Sign ℚ
inst✝³ : Subtraction ℚ
inst✝² : Reciprocation ℚ
inst✝¹ : Division ℚ
inst✝ : Order ℚ
p q : ℚ
OneOfThree : Prop := AA.OneOfThree (p < q) (p ≃ q) (p > q)
this : OneOfThree
⊢ p ≤ q ∨ q ≤ p
no goals