ring_nf
a b c : ℤα
h : b ≠ 0
bound :
  ↑normSq
      (OneHom.toFun (↑↑inclusion) a / OneHom.toFun (↑↑inclusion) b -
        OneHom.toFun (↑↑inclusion) (nearestℤα (OneHom.toFun (↑↑inclusion) a / OneHom.toFun (↑↑inclusion) b))) <
    1
⊢ OneHom.toFun (↑↑inclusion) a / OneHom.toFun (↑↑inclusion) b -
      OneHom.toFun (↑↑inclusion) (nearestℤα (OneHom.toFun (↑↑inclusion) a / OneHom.toFun (↑↑inclusion) b)) =
    (OneHom.toFun (↑↑inclusion) a -
        OneHom.toFun (↑↑inclusion) (nearestℤα (OneHom.toFun (↑↑inclusion) a / OneHom.toFun (↑↑inclusion) b)) *
          OneHom.toFun (↑↑inclusion) b) *
      sorryAx ℂ true
a b c : ℤα
h : b ≠ 0
bound :
  ↑normSq
      (OneHom.toFun (↑↑inclusion) a / OneHom.toFun (↑↑inclusion) b -
        OneHom.toFun (↑↑inclusion) (nearestℤα (OneHom.toFun (↑↑inclusion) a / OneHom.toFun (↑↑inclusion) b))) <
    1
⊢ OneHom.toFun (↑↑inclusion) a * (OneHom.toFun (↑↑inclusion) b)⁻¹ -
      OneHom.toFun (↑↑inclusion) (nearestℤα (OneHom.toFun (↑↑inclusion) a * (OneHom.toFun (↑↑inclusion) b)⁻¹)) =
    OneHom.toFun (↑↑inclusion) a * sorryAx ℂ true -
      OneHom.toFun (↑↑inclusion) b *
          OneHom.toFun (↑↑inclusion) (nearestℤα (OneHom.toFun (↑↑inclusion) a * (OneHom.toFun (↑↑inclusion) b)⁻¹)) *
        sorryAx ℂ true