reserve x, y for object, X, X1, X2 for set;
reserve Y, Y1, Y2 for complex-functions-membered set,
  c, c1, c2 for Complex,
  f for PartFunc of X,Y,
  f1 for PartFunc of X1,Y1,
  f2 for PartFunc of X2, Y2,
  g, h, k for complex-valued Function;

theorem
  g (/) -c = (-g) (/) c
proof
  thus g (/) -c = - (g(/)c) by Th31
    .= (-g) (/) c by Th30;
end;
