Induction on an if-then statement So we are told to do induction on this statement: **"Let P(n) be the statement: If a + n = c + n, then a = b."** , and I am told to induct on n, so I do. Base: Let P(0) be the statement : "If a + 0 = c + 0, then a = b". which is true. From there, you assume P(n) to be true for n (denoted n'). However, I'm stuck on how to go on from here as well as what my inductive hypothesis is. Thanks all!

Any time you're trying to do a proof, you need to look at what your premises are. If you're trying to prove this in Peano arithmetic, then you have the axiom that (a = b) => (a+1=b+1). So if (a+n)=(b+n), then (a+n)+1=(b+n)+1, and by associativity a+(n+1)=b+(n+1).