reserve x,y,z,X,Y for set;
reserve X,Y for non empty set,
  f for Function of X,Y;
reserve X, Y for non empty set,
  F for (BinOp of Y),
  B for (Element of Fin X),
  f for Function of X,Y;
reserve A for set,
  x,y,z for Element of Fin A;
reserve X,Y for non empty set,
  A for set,
  f for (Function of X, Fin A),
  i,j,k for (Element of X);

theorem
  FinUnion({.i,j,k.},f) = f.i \/ f.j \/ f.k
proof
  FinUnion A is idempotent & FinUnion A is commutative by Th34,Th35;
  hence FinUnion({.i,j,k.},f) = FinUnion A.(FinUnion A.(f.i, f.j), f.k) by Th16
,Th36
    .= FinUnion A.(f.i \/ f.j, f.k) by Def4
    .= f.i \/ f.j \/ f.k by Def4;
end;
