Ok, how about I define a new property that my superset contains a 'rainbow' of colors. The subset has only one of the colors, it doesn't contain the rainbow pr

Ok, how about I define a new property that my superset contains a 'rainbow' of colors. The subset has only one of the colors, it doesn't contain the rainbow property. The original post claimed that the superset always has the same or fewer properties. I was questioning whether this was true. You've mentioned that it is generally true, which seems like a better way to describe the concept. -- edit: I understand now, in my example above the subset must contain a property by which it could be identified. The original rainbow property is lost but a new one is gained.