have : q < p ∨ q ≃ p :=
  match ‹p > q ∨ p ≃ q› with
  | Or.inl (_ : p > q) =>
    have : q < p := ‹p > q›
    Or.inl this
  | Or.inr (_ : p ≃ q) =>
    have : q ≃ p := eqv_symm ‹p ≃ q›
    Or.inr 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
x✝ : p > q ∨ p ≃ q
⊢ p ≥ q
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
x✝ : p > q ∨ p ≃ q
this : q < p ∨ q ≃ p
⊢ p ≥ q