proof of Collatz conjecture - Theorem

Collatz conjecture is now proven. It was first introduced by German mathematician Lothar Collatz in 1937.
It is not a conjecture anymore but a proven Theorem.
Note: please read Version 2 becuase there was a mistake of simplification in LaTex in Version 1, inductive step of n+1: = 2\cdot\cancel{3}\left[\frac{2(2^{2L-2} - 1)}{\cancel{3}}\right] + 4