Where in the Laws of the Game does it say that when a player is sent off and shown the red card, that that team must play with one less player.

This is something everyone knows, and I have found it in Advice to Referees, but I can’t find it in the Laws of the Game.

Would a team be able to later challenge the referees’ decision to “play short”?

USSF answer (May 14, 2008):
There has been no change in the Law nor in the interpretation of the Law since we published this answer on May 5, 2003:

Simplification is everything, or so the IFAB thought back in 1997. Believing that everyone “knew” this to be so, they eliminated the phrase from the Laws. And that is why USSF issued this position paper back in 1999:
No Replacement for Player Sent Off after the Game Has Started
International Football Association Board (IFAB) Decision (3), on Law III, formerly stated: “A player who has been ordered off after play has started may not be replaced,” containing this prohibition was omitted by the IFAB in the extensive revision of the Laws that took place in 1997. The rewrite was extensive and included both new language and revisions of existing language: numerous provisions in the 1996 edition of the Laws of the Game were removed and have not reappeared in subsequent revisions. Nevertheless, the provisions of IFAB Decision 3 on Law III (and numerous other decisions) remain valid to this day.
The intention of IFAB was to clarify and simplify concepts, to replace older terminology, to present concepts which are more easily translated into languages other than English and to shorten the Laws of the Game overall. The excised IFAB decisions should not be considered a rejection of the requirement, but an affirmation that a separate, additional statement of the concept involved was unnecessary. In other words, the IFAB believed that the basic principle that a player sent off after the game has started may not be replaced was so well understood by the entire soccer community that it did not need to be mentioned in the Laws.
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