Therefore, ra and rb overlap exactly the same entities

To see that the inference from (17) to (18) is valid, suppose that object o is exactly located at regions ra and rb. Since o is exactly located at ra, o is (by (17)) weakly located at all and only the entities that overlap ra. Likewise, since o is exactly located at rb, o is weakly located at all and only the entities that overlap rb. So ra overlaps a given entity if and only if o is weakly located at that entity; and rb overlaps a given entity if and only if o is weakly located at that entity.