= Solution
Flatten the days, emit both participants of every match and remove repeated names:
``
teams :: [[Match]] -> [Team]
teams days = unique [t | Match a _ b _ <- concat days, t <- [a,b]]
where
unique [] = []
unique (t:ts) = t : unique (filter (/= t) ts)
``
Every emitted name belongs to some match, and every participating team enters the intermediate <list>. At each recursive step, `unique` emits its first remaining name once and deletes precisely its later occurrences. <Induction> therefore proves both coverage and absence of duplicates. The output preserves first appearance; no particular team ordering was required. This simple <list> implementation can take quadratic time in the number of participant occurrences, which is permissible here; the question imposes no efficiency target.
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