  The fact that the null generators of a future Cauchy horizon are past
complete was proved first by Hawking and Ellis [1]. Then Budzy\'nski,
Kondracki, and Kr\'olak outlined a proof free from an error found in the
original one [2]. Finally, a week ago Minguzzi published his version of proof
[3] patching a previously unnoticed hole in the preceding two. I am not aware
of any flaws in that last proof, but it is quite difficult. In this note I
present a simpler one.
