OK , um , so I think the middle block doesn't really give you any more information , ex than the top block. And the bottom block similarly only just illus you know , all it does is illustrate that you can drop the subscripts and  and that you can drop the , um  uh , that you can give dual types. Oh , one thing I should mention is about " designates ". I think I 'm actually inconsistent across these as well. So , um , strike out the M subscript on the middle block.
Mm - hmm.
So basically now , um , this is actually  this little change actually goes along with a big linguistic change , which is that " designates " isn't only something for the semantics to worry about now.
Good.