Hello,

I'm trying to formalize some properties of tuples and I find some problems for relating the elements of the tuple.

I have the tuple at time defined as , where:

- is a set of elements at time

- is a set of elements at time

- is a set of elements at time

- , where if and are related.

- , where if and are related.

- , where if and are related.

Now, I want to represent that: if at time , there is a relationship that is 1 between and , and a relationship that is 1 between and , then it must exists a relationship between and that is also 1. I don't really know how to write it. I first tried:

I think this option is not mathematically correct because is not a set. May the next option be more correct??

I don't know how to say it. I would be very grateful If you could help me.

Thank you.