Hello!

If I understand correctly, the first set is easy to define.

Having a parameter tn and then having a set defined as {1..tn} would do the trick. You may want to put a condition in the definition, something like

If tn >= 1 then

{1..tn}

endif;

To avoid getting errors when tn is < 1.

For the second one, I am not sure if I fully understand. Do you have an indexed set? Which t are you referring to when you mention  ∀τ =t+1,...,min(t+Li −1,tn)? Since t is an index of a set, it is variable, not a fixed parameter.

Maybe a parameter could do the trick, something like:

tau(t1,t2)

defined as
if t2 > t1 and t2 < min(t + Li - 1,tn) then 1 endif;

Assuming Li is a parameter.

This is the code I played around with:

Parameter tn;

Parameter Li;

Set sT {
    SubsetOf: Integers;
    Index: t, t1, t2;
    Property: ElementsAreNumerical;
    Definition: {
        if tn >= 1 then
            {1..tn}
        endif;
    }
}

Parameter Tau {
    IndexDomain: (t1,t2);
    Definition: {
        if t2 > t1 and t2 < min(t1 + Li - 1,tn) then 1 endif;
    }
}
 

And using tn = 10; Li = 5; I would get:

Hope it helps.