have near := add_le_add hre him
a b c : ℤα
z : ℂ
hre : (z - OneHom.toFun (↑↑inclusion) (nearestℤα z)).re ^ 2 ≤ 2⁻¹ ^ 2
him : (z - OneHom.toFun (↑↑inclusion) (nearestℤα z)).im ^ 2 ≤ (4⁻¹ * rt7) ^ 2
arith : 2⁻¹ ^ 2 + (4⁻¹ * rt7) ^ 2 < 1
⊢ (z.re - (↑inclusion (nearestℤα z)).re) ^ 2 + (z.im - (↑inclusion (nearestℤα z)).im) ^ 2 < 1
a b c : ℤα
z : ℂ
hre : (z - OneHom.toFun (↑↑inclusion) (nearestℤα z)).re ^ 2 ≤ 2⁻¹ ^ 2
him : (z - OneHom.toFun (↑↑inclusion) (nearestℤα z)).im ^ 2 ≤ (4⁻¹ * rt7) ^ 2
arith : 2⁻¹ ^ 2 + (4⁻¹ * rt7) ^ 2 < 1
near :
  (z - OneHom.toFun (↑↑inclusion) (nearestℤα z)).re ^ 2 + (z - OneHom.toFun (↑↑inclusion) (nearestℤα z)).im ^ 2 ≤
    2⁻¹ ^ 2 + (4⁻¹ * rt7) ^ 2
⊢ (z.re - (↑inclusion (nearestℤα z)).re) ^ 2 + (z.im - (↑inclusion (nearestℤα z)).im) ^ 2 < 1