This is a simple question about writing but I'm a little bit confused now about the logic in using "consistent with". The context is as follows:
We first derive a formula for a special case, say, for $i=2$. Later we derive a formula for general cases, say, for $i=3,4,5...$, which is actually also true for $i=2$. Shall we say "the formula for $i=2$ is consistent with the general formula" or "the general formula is consistent with the special case($i=2$) before" ?
Reference to some existing texts would be much appreciated. Thanks a lot.
Well in this case you should say that the case of i=2 is consistent with the general formula. The reason why is because you are taking note of a particular example, that holds true. So because it holds true, this is consistent with your theorem that it holds for i=1,2,3.. etc