Building a skeletal multi file sketch fails -- why?

Can't get a multi-file/multi-tab project to build. I created a skeleton sketch to test multi-file building, and even this simple conception fails to build.

== Compiler/linker error: =============================
libkoe.cpp.o: In function loop': C:\Users\X\AppData\Local\Temp\build6301035900337716840.tmp/libkoe.cpp:11: undefined reference to lib_loop()'
libkoe.cpp.o: In function setup': C:\Users\X\AppData\Local\Temp\build6301035900337716840.tmp/libkoe.cpp:7: undefined reference to lib_setup()'
===================================================

Source files/tabs:

=== libtest: (main file)===========================
#include "lib.h"

void setup() {
lib_setup();
}

void loop() {
lib_loop();
}

=== lib.h: =======================================
#ifndef LIB_H
#define LIB_H
void lib_setup();
void lib_loop();
#endif

=== lib.c: =======================================
#include "lib.h"

void lib_setup() {
}

void lib_loop() {
}
======================================

Are there some settings to tweak to get this going?
Should I use C++ style source files when creating multi-file projects?
Something messed up in my environment?

Originally I tried to create a library (in libraries directory).

thanks for your time!

The key is in this line:

=== lib.c: =======================================

Rename the file to have a .cpp extension, instead.

PaulS:
The key is in this line:

=== lib.c: =======================================

Rename the file to have a .cpp extension, instead.

Thanks, Paul!

Problem solved!

It would have taken me a while to figure that one out myself!