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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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    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...2012-03-19

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