Comment on arXiv:2202.01553: The Distribution of a Gaussian Covariate Statistic

This is a comment on arXiv:2202.01553. In regression Gaussian covariate p-values (Davies and D{ü}mbgen, arXiv:2202.01553) are used to control greedy forward subset selection by accounting for choosing the best when fitting many variables. Here we outline a simple proof of their Theorems 1 and 2, making alterations to simplify the exposition by including a new variable rather than excluding an included variable and some slight changes in notation.