no goals
R : Type ?u.55685
A : Type ?u.55688
K : Type u_2
inst✝¹⁰ : CommRing R
inst✝⁹ : CommRing A
inst✝⁸ : Field K
inst✝⁷ : IsDomain A
R₁ : Type u_1
inst✝⁶ : CommRing R₁
inst✝⁵ : IsDomain R₁
inst✝⁴ : Algebra R₁ K
inst✝³ : IsFractionRing R₁ K
I J : FractionalIdeal R₁⁰ K
K' : Type ?u.56699
inst✝² : Field K'
inst✝¹ : Algebra R₁ K'
inst✝ : IsFractionRing R₁ K'
x : R₁
hx : x ≠ 0
⊢ ↑(Ideal.span {x}) * (↑(Ideal.span {x}))⁻¹ = 1
rw [coeIdeal_span_singleton,
  spanSingleton_mul_inv K <|
    (map_ne_zero_iff _ <| NoZeroSMulDivisors.algebraMap_injective R₁ K).mpr hx]