map length (tiers :: [[ Nat->Nat->Nat ]])  =  [1,1,5,13,...]

length (list :: [ Nat->Nat->Nat ])  =  Infinity

allUnique (list :: [ Nat->Nat->Nat ])  =  True

ratioRepetitions (list :: [ Nat->Nat->Nat ])  =  0 % 1

tiers :: [Nat->Nat->Nat]  =
  [ [ \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 0
                (0,2) -> 0
                (1,1) -> 0
                (2,0) -> 0
                (0,3) -> 0
                (1,2) -> 0
                ...
    ]
  , [ \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 1
                (1,0) -> 1
                (0,2) -> 1
                (1,1) -> 1
                (2,0) -> 1
                (0,3) -> 1
                (1,2) -> 1
                ...
    ]
  , [ \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 1
                (1,0) -> 0
                (0,2) -> 1
                (1,1) -> 0
                (2,0) -> 0
                (0,3) -> 1
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 1
                (0,2) -> 0
                (1,1) -> 1
                (2,0) -> 1
                (0,3) -> 0
                (1,2) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 0
                (1,0) -> 1
                (0,2) -> 0
                (1,1) -> 0
                (2,0) -> 1
                (0,3) -> 0
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 1
                (1,0) -> 0
                (0,2) -> 1
                (1,1) -> 1
                (2,0) -> 0
                (0,3) -> 1
                (1,2) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 2
                (0,1) -> 2
                (1,0) -> 2
                (0,2) -> 2
                (1,1) -> 2
                (2,0) -> 2
                (0,3) -> 2
                (1,2) -> 2
                ...
    ]
  , [ \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 0
                (1,0) -> 0
                (0,2) -> 0
                (1,1) -> 0
                (2,0) -> 0
                (0,3) -> 0
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 1
                (1,0) -> 0
                (0,2) -> 1
                (1,1) -> 0
                (2,0) -> 0
                (0,3) -> 1
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 2
                (0,1) -> 2
                (1,0) -> 0
                (0,2) -> 2
                (1,1) -> 0
                (2,0) -> 0
                (0,3) -> 2
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 1
                (0,2) -> 0
                (1,1) -> 1
                (2,0) -> 0
                (0,3) -> 0
                (1,2) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 1
                (1,0) -> 0
                (0,2) -> 1
                (1,1) -> 0
                (2,0) -> 1
                (0,3) -> 1
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 1
                (0,2) -> 0
                (1,1) -> 0
                (2,0) -> 1
                (0,3) -> 0
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 0
                (0,2) -> 0
                (1,1) -> 1
                (2,0) -> 0
                (0,3) -> 0
                (1,2) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 0
                (1,0) -> 2
                (0,2) -> 0
                (1,1) -> 2
                (2,0) -> 2
                (0,3) -> 0
                (1,2) -> 2
                ...
    , \x y -> case (x,y) of
                (0,0) -> 2
                (0,1) -> 0
                (1,0) -> 2
                (0,2) -> 0
                (1,1) -> 0
                (2,0) -> 2
                (0,3) -> 0
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 1
                (1,0) -> 0
                (0,2) -> 0
                (1,1) -> 1
                (2,0) -> 0
                (0,3) -> 0
                (1,2) -> 0
                ...
    , \x y -> case (x,y) of
                (0,0) -> 1
                (0,1) -> 0
                (1,0) -> 1
                (0,2) -> 1
                (1,1) -> 0
                (2,0) -> 1
                (0,3) -> 1
                (1,2) -> 1
                ...
    , \x y -> case (x,y) of
                (0,0) -> 0
                (0,1) -> 2
                (1,0) -> 0
                (0,2) -> 2
                (1,1) -> 2
                (2,0) -> 0
                (0,3) -> 2
                (1,2) -> 2
                ...
    , \x y -> case (x,y) of
                (0,0) -> 3
                (0,1) -> 3
                (1,0) -> 3
                (0,2) -> 3
                (1,1) -> 3
                (2,0) -> 3
                (0,3) -> 3
                (1,2) -> 3
                ...
    ]
  , ...
  ]