After a Windows reboot cygwin became quite broken, gcc would not work
for instance. It turns out that somehow the mounts became broken.
Here are the mounts that should be seen by a user.

$ cat mount.out
C:/cygwin/bin on /usr/bin type ntfs (binary,auto)
C:/cygwin/lib on /usr/lib type ntfs (binary,auto)
C:/cygwin on / type ntfs (binary,auto)

Note how /bin and /lib are re-mounted on /usr/bin and /usr/lib. No
idea why that is.