case mpr =>
  intro (min_max : min p r ≤ q ∧ q ≤ max p r)
  show p⊣ q ⊢r
  have : p ≤ r ∨ r ≤ p := le_dichotomy
  have : p ≤ q ∧ q ≤ r ∨ r ≤ q ∧ q ≤ p :=
    match ‹p ≤ r ∨ r ≤ p› with
    | Or.inl (_ : p ≤ r) =>
      have : p ≤ q ∧ q ≤ r := order_from_min_max min_max ‹p ≤ r›
      Or.inl this
    | Or.inr (_ : r ≤ p) =>
      have : min r p ≤ q ∧ q ≤ max r p := min_max_comm min_max
      have : r ≤ q ∧ q ≤ p := order_from_min_max this ‹r ≤ p›
      Or.inr this
  have : p⊣ q ⊢r := between_order.mpr ‹p ≤ q ∧ q ≤ r ∨ r ≤ q ∧ q ≤ p›
  exact this
ℕ ℤ ℚ : Type
inst✝¹² : Natural ℕ
inst✝¹¹ : Integer ℤ
inst✝¹⁰ : Core ℚ
inst✝⁹ : Addition ℚ
inst✝⁸ : Negation ℚ
inst✝⁷ : Subtraction ℚ
inst✝⁶ : Multiplication ℚ
inst✝⁵ : Reciprocation ℚ
inst✝⁴ : Division ℚ
inst✝³ : Sign ℚ
inst✝² : Order ℚ
inst✝¹ : MinMax ℚ
inst✝ : Metric ℚ
p q r : ℚ
⊢ Ordered.min p r ≤ q ∧ q ≤ Ordered.max p r → p⊣ q ⊢r
no goals