case mp =>
  intro (_ : p ≥ q)
  show p > q ∨ p ≃ q
  have : q ≤ p := ‹p ≥ q›
  have : q < p ∨ q ≃ p := le_cases.mp this
  match this with
  | Or.inl (_ : q < p) =>
    have : p > q := ‹q < p›
    have : p > q ∨ p ≃ q := Or.inl this
    exact this
  | Or.inr (_ : q ≃ p) =>
    have : p ≃ q := eqv_symm ‹q ≃ p›
    have : p > q ∨ p ≃ q := 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
⊢ p ≥ q → p > q ∨ p ≃ q
no goals