case mp =>
  intro (_ : p⊣ q ⊢r)
  show min p r ≤ q ∧ q ≤ max p r
  have : p ≤ q ∧ q ≤ r ∨ r ≤ q ∧ q ≤ p := between_order.mp ‹p⊣ q ⊢r›
  match this with
  | Or.inl (_ : p ≤ q ∧ q ≤ r) =>
    have : min p r ≤ q ∧ q ≤ max p r := min_max_from_order ‹p ≤ q ∧ q ≤ r›
    exact this
  | Or.inr (_ : r ≤ q ∧ q ≤ p) =>
    have : min r p ≤ q ∧ q ≤ max r p := min_max_from_order ‹r ≤ q ∧ q ≤ p›
    have : min p r ≤ q ∧ q ≤ max p r := min_max_comm this
    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
⊢ p⊣ q ⊢r → Ordered.min p r ≤ q ∧ q ≤ Ordered.max p r
no goals