convert (primesBetween_le 1 N (N ^ (1/2 : ℝ)) (by norm_num) (by norm_cast; omega)
  (Real.one_lt_rpow (by norm_cast; omega) (by norm_num))) using 1
x y z : ℝ
hx : 0 < x
hy : 0 < y
hz : 1 ≤ z
N : ℕ
hN✝ : ¬N = 0
hN : ¬N = 1
⊢ ↑(primesBetween 1 (1 + ↑N)) ≤ 2 * (↑N / (↑N ^ (1 / 2)).log) + 6 * (↑N ^ (1 / 2) * (1 + (↑N ^ (1 / 2)).log) ^ 3)
case h.e'_4
x y z : ℝ
hx : 0 < x
hy : 0 < y
hz : 1 ≤ z
N : ℕ
hN✝ : ¬N = 0
hN : ¬N = 1
⊢ 2 * (↑N / (↑N ^ (1 / 2)).log) + 6 * (↑N ^ (1 / 2) * (1 + (↑N ^ (1 / 2)).log) ^ 3) =
    2 * ↑N / (↑N ^ (1 / 2)).log + 6 * ↑N ^ (1 / 2) * (1 + (↑N ^ (1 / 2)).log) ^ 3