Remember that any time you write down a series of mathematical expressions, you need linking symbols or words to explain how they are related. For example, you might say:

    "A = B because blah
         which equals C because blahblah"
         etc.

A problem that often comes up in proofs of an induction step, is that people just write something like:

   A
   B
   C

where A, B, and C are simple statements involving some mathematics (like an equation or a statement that a certain expression is divisible by 5). Often what is going on is that A is the thing that we want to prove in the induction step, and the intention is to say "I want to show A. We can see that A is equivalent to B, and then we can see that B is equivalent to C." If C is clearly true, and it's clear (or explained) why A is equivalent to B and B is equivalent to C, then you're set, but you need to include the words that show this is what you are doing.

If you don't include anything but the list of statements, I would be forced to read a "proof" like the above as "We know A. From A, we can conclude B. Then, from B, we can conclude C." But if there isn't actually a reason why we know A, or C is not what we are trying to prove, then this is not a proof.

So a good proof that C follows from A could look something like this:

 We are given A.
 Then B follows by rule X.
 This implies C because of Y.

or it could be like this:

 We want to show C.
 B is equivalent to C because of X.
 A is equivalent to B because of Y.
 A is clearly true, so we have proven C is true.