In a theorem that I am trying to prove I first use proof by contradiction and for reaching contradiction I need to prove using cases.
Now for formally writing proof by contradiction we use the following structure -
Method: In order to prove a proposition P by contradiction: 1. Write, “We use proof by contradiction.” 2. Write, “Suppose P is false.” 3. Deduce something known to be false (a logical contradiction). 4. Write, “This is a contradiction. Therefore, P must be true.”
I have the doubt that how do I incorporate a statement that I will use proof by cases when I actually am not going to prove the statement true but want to reach a contradiction in each of the cases.
I have figured out the proof but do not understand how to present it correctly.