I went for the cruder proof of actually working it out for a small number - 4 teams, each plays the other H&A, total of 12 matches.

For n teams, the number of matches per matchday is n/2, the number of matchdays is (n/2)(n-1), and the number of matches is n(n-1). In this case it's 4x3=12 matches, for 20 teams it's 20x19=380.

wk1 wk2 wk3 wk4 wk5 wk6

AB AC AD BA CA DA

CD BD BC DC DB CB