Proving one proves all

In this document, the argumentation that the Collatz conjecture is true will be presented step by step. First the statement of the problem will be described, followed by the1st theorem: The Collatz Conjecture can be proven true using only the positive odd integers, as the conjecture's validity for odd numbers implies its validity for even numbers due to their eventual reduction to odd numbers through repeated division by 2. The 2nd theorem: For all positive integers m, n, the sequences generated by the expression 2^ (2m-1) n- (2^ (2m-1) +1) /3 will reach 3n-1 after applying the Collatz function. 3rd theorem: For all integers m, n, the sequences generated by the expression 2^ (2m-1) n- (2^ (2m-1) +1) /3 share the value of the first term generated by the last known sequence which is generated by the same expression. The 4th theorem: Only the sequence (4ᵐ-1) /3 is needed to prove the Collatz conjecture. The 5th theorem: The Collatz conjecture is true.