reserve A, B for non empty set,
  A1, A2, A3 for non empty Subset of A;
reserve X for TopSpace;
reserve X for non empty TopSpace;
reserve X1, X2 for non empty SubSpace of X;
reserve X0, X1, X2, Y1, Y2 for non empty SubSpace of X;
reserve X, Y for non empty TopSpace;
reserve f for Function of X,Y;
reserve X,Y,Z for non empty TopSpace;
reserve f for Function of X,Y,
  g for Function of Y,Z;
reserve X, Y for non empty TopSpace,
  X0 for non empty SubSpace of X;
reserve f for Function of X,Y;
reserve f for Function of X,Y,
  X0 for non empty SubSpace of X;
reserve X, Y for non empty TopSpace,
  X0, X1 for non empty SubSpace of X;
reserve f for Function of X,Y,
  g for Function of X0,Y;
reserve X0, X1, X2 for non empty SubSpace of X;
reserve f for Function of X,Y,
  g for Function of X0,Y;
reserve X for non empty TopSpace,
  H, G for Subset of X;
reserve A for Subset of X;
reserve X0 for non empty SubSpace of X;
reserve X, Y for non empty TopSpace;
reserve X1, X2 for non empty SubSpace of X;
reserve X, Y for non empty TopSpace;

theorem
  for X1, X2 being non empty SubSpace of X, f1 being Function of X1,Y,
f2 being Function of X2,Y st X1 misses X2 or f1|(X1 meet X2) = f2|(X1 meet X2)
  holds f1 union f2 = f2 union f1
proof
  let X1, X2 be non empty SubSpace of X, f1 be Function of X1,Y, f2 be
  Function of X2,Y;
  assume X1 misses X2 or f1|(X1 meet X2) = f2|(X1 meet X2);
  then (f1 union f2)|X1 = f1 & (f1 union f2)|X2 = f2 by Def12;
  hence thesis by Th126;
end;
