Standar Library Support Question

Hello. This is a very basic question. However I am new at the cross compilation scene, and I ask to bare with me.

I've been reading about compiling toolchains for arm. One thing that keeps coming up is the need to have a certain library (for example stdio) for a given operating system. I've rencently succesfully (as in there were no errors or warnings) compiled a Hello World application for a Cortex M0, using uVision MDK-Lite Version 5.11. I manually set the memory ranges in the target dialog box and used the offered Device startup sources (startup_ARMCM0.s and system_ARMCM0.c) provided by the program. As I understood this was a bare metal project. No OS. I haven't had the chance yet. But were I to download this to a M0 platform, It would run. But It got me thinking. What is it including really when I write the line

#include<stdio.h>

Am I wrong and Keil IS assuming a OS? Does Keil have certain libraries for Different OS possibilities?

Thanks for understanding and any clarification.