case mpr =>
  intro (_ : p ≤ q)
  show max p q ≃ q
  have : max p q ≃ p ∨ max p q ≃ q := max_cases
  match this with
  | Or.inl (_ : max p q ≃ p) =>
    have : q ≤ max p q := max_leR
    have : q ≤ p := le_substR_eqv ‹max p q ≃ p› ‹q ≤ max p q›
    have : p ≃ q := le_antisymm ‹p ≤ q› ‹q ≤ p›
    have : max p q ≃ q := eqv_trans ‹max p q ≃ p› ‹p ≃ q›
    exact this
  | Or.inr (_ : max p q ≃ q) =>
    have := ‹max p q ≃ q›
    exact this
ℕ ℤ ℚ : Type
inst✝¹¹ : Natural ℕ
inst✝¹⁰ : Integer ℤ
inst✝⁹ : Core ℚ
inst✝⁸ : Addition ℚ
inst✝⁷ : Multiplication ℚ
inst✝⁶ : Negation ℚ
inst✝⁵ : Sign ℚ
inst✝⁴ : Subtraction ℚ
inst✝³ : Reciprocation ℚ
inst✝² : Division ℚ
inst✝¹ : Order ℚ
inst✝ : MinMax ℚ
p q : ℚ
⊢ p ≤ q → Ordered.max p q ≃ q
no goals