I am looking to specify something in Isabelle of the form that there exists a $j$ such that $lb < j < ub$, where $lb$ and $ub$ are lower and upper bounds.
For a single condition, we can say, for example, $\exists j < ub . P(j)$ in Isabelle. How to specify both conditions on j? Is it right to say both conditions in the following manner: $\exists j < ub. \exists j > lb. P(j)$?
Note that I am not looking for something like $\exists j. (j > lb \wedge j < ub). P(j) $, because Isabelle does not allow me to use the second "such that" symbol ".".
