Please help me find an error in this proof attempt of the notorious Collatz Conjecture. Note that the proof is unrevised and is likely to contain an error. Also, I have very little training and experience writing formal mathematics.

Define any progressive odd integer such that it belongs to the set 3+4n and any regressive odd integer such that it belongs to the set 1+4n where n is the set of all natural numbers. In this way any progressive odd always yields an odd result and any regessive odd yields an even result. In the paper the function is redefined in such terms.

Thank you for your help.