q✝ : ℚ
x y : ℝ
h : Irrational x
q : ℚ
hq : q ≠ 0
⊢ Irrational (x * ↑q⁻¹)
q✝ : ℚ
x y : ℝ
h : Irrational x
q : ℚ
hq : q ≠ 0
⊢ Irrational (x / ↑q)
rw [div_eq_mul_inv, ← cast_inv]
no goals
q✝ : ℚ
x y : ℝ
h : Irrational x
q : ℚ
hq : q ≠ 0
⊢ Irrational (x * ↑q⁻¹)
exact h.mul_rat (inv_ne_zero hq)