apply primesBetween_mono_right
x y z : ℝ
hx : 0 < x
hy : 0 < y
hz : 1 ≤ z
N : ℕ
hN✝ : ¬N = 0
hN : ¬N = 1
h : ↑(primesBetween 1 (1 + ↑N)) ≤ 2 * (↑N / (↑N ^ (1 / 2)).log) + 6 * (↑N ^ (1 / 2) * (1 + (↑N ^ (1 / 2)).log) ^ 3)
⊢ primesBetween 1 ↑N ≤ primesBetween 1 ↑(1 + N)
case hbc
x y z : ℝ
hx : 0 < x
hy : 0 < y
hz : 1 ≤ z
N : ℕ
hN✝ : ¬N = 0
hN : ¬N = 1
h : ↑(primesBetween 1 (1 + ↑N)) ≤ 2 * (↑N / (↑N ^ (1 / 2)).log) + 6 * (↑N ^ (1 / 2) * (1 + (↑N ^ (1 / 2)).log) ^ 3)
⊢ ↑N ≤ ↑(1 + N)