That header is supplied by the compiler, not the library! This is explained in the GCC manual as follows:
The ISO C standard defines (in clause 4) two classes of conforming
implementation. A conforming hosted implementation supports the
whole standard including all the library facilities; a conforming
freestanding implementation is only required to provide certain
library facilities: those in <float.h>, <limits.h>,
<stdarg.h>, and <stddef.h>; since AMD1, also those in
<iso646.h>; since C99, also those in <stdbool.h> and
<stdint.h>; and since C11, also those in <stdalign.h>
and <stdnoreturn.h>. In addition, complex types, added in C99, are not
required for freestanding implementations.