Sure, but in the situation we were talking about, the user never wrote a definition for write(), and the user did not specify any library to include that provided a definition of write(). From the standard's perspective, that means there is no definition for it in the entire program.
Keep in mind that the standard's perspective is somewhat different from how things work in practice. We know that on Unix-like systems, there is also the concept of libraries, somewhat different from how the standard describes it, and write() will be provided by the "c" library. But consider the following strictly conforming program:
#include <stdio.h>
void write(void) {
puts("Hello, world!");
}
int main(void) {
write();
}
A confirming C implementation is not allowed to reject this for a duplicate definition of write(): the name "write" is reserved for use by the programmer, it is not reserved to the implementation. This program must be considered not to violate the "there shall be exactly one external definition for the identifier", so the only way to consider this valid is to say that the implementation does not implicitly provide an external definition of the write() function as far as the C standard is concerned.
Yet at the same time, from the perspective of the implementation, the c library is considered to provide a definition of the write() function, but it is a definition that is only used if the program does not override it with another definition that should be used instead. This concept of multiple definitions for the same name, with rules specifying which of the multiple definitions gets picked, is very useful but is also beyond the scope of the C standard. When we say that a function is defined, we need to be clear on whether we use "define" in the ISO C sense or in some other sense. As your comment shows, things get very confusing if we are not careful with that.