Point at which Prime-Counting Function becomes less than Eulerian Logarithmic Integral/Using Riemann Hypothesis

Theorem
Let $\map \pi n$ denote the prime-counting function.

Let $a \uparrow b$ be interpreted as Knuth notation for $a^b$.

Suppose the Riemann Hypothesis holds.

Then:
 * $\exists n < 10 \uparrow \paren {10 \uparrow \paren {10 \uparrow 34} }: \map \pi n - \displaystyle \int_2^n \frac {\d x} {\ln x} < 0$

Here, $10 \uparrow \paren {10 \uparrow \paren {10 \uparrow 34} }$ is Skewes' number.