Including headers

Is it wrong to take it for granted that some standard headers include others?
An example would be iostream which seems to include iomanip, ostream, istream and ios, etc.

To rephrase the question: is it good practice to be paranoid and include all needed headers?
It would make the most sense. You never know what you're going to need in a program.
Yes, if it's not obvious that they are included. For example, you don't need to include ostream or istream if you already included iostream.
Don't sweat the small stuff.
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