have atLeastOne : AA.OneOfThree (p < q) (p ≃ q) (p > q) := this.rotR
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
spq : ℤ := sgn (p - q)
this✝ : AA.OneOfThree (spq ≃ 0) (spq ≃ 1) (spq ≃ -1)
this : AA.OneOfThree (p ≃ q) (p > q) (p < q)
⊢ AA.ExactlyOneOfThree (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
spq : ℤ := sgn (p - q)
this✝ : AA.OneOfThree (spq ≃ 0) (spq ≃ 1) (spq ≃ -1)
this : AA.OneOfThree (p ≃ q) (p > q) (p < q)
atLeastOne : AA.OneOfThree (p < q) (p ≃ q) (p > q)
⊢ AA.ExactlyOneOfThree (p < q) (p ≃ q) (p > q)