If, during a line of reasoning, you change the definitions of what you are talking about, you can prove anything.

If someone is trying to follow your argument and they ask you to define what you mean by something, you could assume they are just too new to the field and not familiar with the widely accepted definitions of common terms.  It could also be that they are trying to follow your logic and they might be detecting a drift in your definitions.

I often find myself trying to divine the definition from the context of the argument. Whether or not an aspect of an argument has been explicitly defined, I find it useful to hold in my mind a concrete picture of an example, when someone is presenting an abstract argument.  I take what has been said and find an example and follow along, seeing how the line of reasoning holds with respect to the example.  

This technique makes definitional drift pop out when the argument doesn't hold for your example.  

If you do this, you can offer your example to the person presenting, showing it as a counterexample.  Or, you might look for a different definition with another example for which the argument still has legs.  In this latter case, you have forced a narrower definition for which the argument applies.

Frequently the person presenting the reasoning is suggesting the conclusion applies to the broader case.  Narrowing the argument to put it on solid footing improves it.