have : sgn (p₂ - q) ≃ -1 := calc
  sgn (p₂ - q) ≃ _ := sgn_subst (sub_substL (eqv_symm ‹p₁ ≃ p₂›))
  sgn (p₁ - q) ≃ _ := ‹sgn (p₁ - q) ≃ -1›
  (-1)         ≃ _ := Rel.refl
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
p₁ p₂ q : ℚ
x✝¹ : p₁ ≃ p₂
x✝ : p₁ < q
this : sgn (p₁ - q) ≃ -1
⊢ p₂ < 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
p₁ p₂ q : ℚ
x✝¹ : p₁ ≃ p₂
x✝ : p₁ < q
this✝ : sgn (p₁ - q) ≃ -1
this : sgn (p₂ - q) ≃ -1
⊢ p₂ < q