The linux kernel also has its own headers (IIRC it was something like <asm/unistd.h> and/or <sys/syscall.h>, but might depend on architecture and version) where it will provide the stub asm statements.

In my memory the syscall ABI has changed a few times (i386 had int $0x80, then sysenter, then abstracting it in the vdso, then amd64 has 'syscall'), so it may be easier to let the kernel header provide the mechanism.

The Linux syscall ABI is (famously) stable; on x86* you can still call into 0x80 just fine. There might be new interfaces made available, but existing programs shouldn't break. Although, in C there could be value in abstracting over the per-platform differences like int/syscall. I've only ever done raw syscalls from assembly where portability was rather moot:)