I know that in fact has basically the meaning of actually and it is used to contrast two sentences:

1They think she is John's girlfriend. In fact she is his cousin.

But I read that it is possible to use in fact to link sentences, which are not in contrast with each other. The first sentence makes a general statement and the following ones, introduced by in fact, explain this general statements with more specific ones.

For examples.
2 Vegetables should play an important role in our diet. In fact, they provide vitamins such as .....; moreover they also provide ....and contain few calories.

in this second case the sentence introduced by in fact and the following ones indicate sopecific arguments which support the general idea stated in the first one.

I often use in fact in this way. Am I right?
If not, which connector would be appropriate? ( indeed??? ; I think it has two meanings exactly like in fact....)
Thanks Rip.