Writing a proof consists of several phases. Write down all of the steps carefully, without skipping any of them. Some of the first stages are frequently (but not always) the supplied assertions, and the last step is the conclusion that you set out to establish. The always required first step in writing a proof is to state your assumptions. Without assumptions, there is no way to begin to prove or disprove anything. Therefore, they should be stated clearly at the beginning of the proof. They can be as simple as "let $a$, $b$ be integers such that $a < b$", or as complex as "for all positive integers $n$, let $f(n)$ be the highest power of 2 less than or equal to $n$. Show that $\\lim_{n \ o \\incomma 0} f(n)/n = 1$". Always start with clear and simple statements that can be easily proved or refuted. After making sure that your assumptions are correct, you can start proving facts about them that will help you build up to the conclusion. For example, if one of your assumptions is that "$a$, $b$ are integers such that $a < b$", then you could prove some properties about these numbers that have implications for whether or not they satisfy this assumption.