Why is stddef.h not in /usr/include?

Question

I have compiled the gnu standard library and installed it in $GLIBC_INST.

Now, I try to compile a very simple programm (using only one #include

Answer 1

When you say #include it does not require that /usr/include/stddef.h exists as a file on disk at all. All that is required of an implementation is that #include works, and that it gives you the features that header is meant to give you.

In your case, the implementation put some of its files in another search path. That's pretty typical.