# Notation of instantiating variables by their value in a constraint set

I have a constraint set $C = \{1 \leq x \leq i, j \leq y \leq j+2\}$, now I would like to get another constraint set $C'$ from $C$ to instantiate all $j$ by a value 5, so $C' = \{1 \leq x \leq i, 5 \leq y \leq 7\}$

I am looking for an elegant way to express the relaion between $C$ and $C'$.

Some suggest $C' = C[j \mapsto 5]$ or $C' = C \leftarrow (j \mapsto 5)$ that I don't find appropriate.

Do you think $C' = C \sqcap \{j = 5\}$ makes sense?

Does anyone have any better idea?

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If you're writing something that you want anyone else to read, the best idea in this case may just be to use words. I doubt there's any existing notation that will be clear to everyone already. If it's really necessary, you can define your own notation, and make it clear that you're using your own notation. –  JohnJamesSmith Mar 19 '12 at 0:50
I agree that I have to define my own notation and explain before using it, but I have to decide which notation makes sense to be defined... –  SoftTimur Mar 19 '12 at 1:03

Well, inspired by that notation used in calculus, you might try $C|_{j=5}$.