There are only three things you need to remember in order to prove a theory. I have not met a lecturer who told me this. Maybe they think that this is trival. But it never failed to draw a blank look from my school mates when I told them about my great discovery.
1st, proof by induction. E.g. the statement "I can only give birth to boys." For n=1, well, my first child is a boy. So the statement is true. Let's take any n. Assume n is true. I use n = 1, I next prove if n+1 is true. In my case, n+1=2, the statement is true. By induction, the statement is true for all n.
2nd, proof by contradiction. I remember the lightning sign or two opposite arrows, my lecturer will draw when this is done. This is the easiest proof. E.g. the statement "All lady bosses are mean." Now, if you can find a lady boss who is not mean. The statement is false.
3rd, proof by first principle. This is the most difficult to prove 'cos you need to prove for all cases. You try to build mini-statements that support the first statement. E.g. "Lady bosses are a mix of mean and nice people." You will first need to split lady bosses into several different baskets - something similar to market segmentation. Then for each basket, you prove either the basket is mean or nice.
Did I not tell you that I will make a good maths teacher? For pre-university level, I will teach my children that a number by itself has no meaning, unless you attach a meaning to it. At university level and beyond, logic tells but story sells.