map length (tiers :: [[ Set Nat3 ]])  =  [1,1,1,2,1,1,1]

length (list :: [ Set Nat3 ])  =  8

allUnique (list :: [ Set Nat3 ])  =  True

ratioRepetitions (list :: [ Set Nat3 ])  =  0 % 1

tiers :: [Set Nat3]  =
  [ [Set []]
  , [Set [0]]
  , [Set [1]]
  , [ Set [0,1]
    , Set [2]
    ]
  , [Set [0,2]]
  , [Set [1,2]]
  , [Set [0,1,2]]
  ]