# How to check if region made by one IntervalBox() contains a region made by another IntervalBox()?

**URL:** https://discourse.julialang.org/t/how-to-check-if-region-made-by-one-intervalbox-contains-a-region-made-by-another-intervalbox/102246
**Category:** General Usage
**Tags:** question, package
**Created:** [July 29, 2023, 5:29pm UTC](https://discourse.julialang.org/t/how-to-check-if-region-made-by-one-intervalbox-contains-a-region-made-by-another-intervalbox/102246 "2023-07-29T17:29:57Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![Ashu](https://avatars.discourse-cdn.com/v4/letter/a/4bbf92/32.png) [@Ashu](https://discourse.julialang.org/u/Ashu)
#### Post date: [July 29, 2023, 5:29pm UTC](https://discourse.julialang.org/t/how-to-check-if-region-made-by-one-intervalbox-contains-a-region-made-by-another-intervalbox/102246/1 "2023-07-29T17:29:58Z")

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Hello,

I want to check if `Z = IntervalBox(-1..1, 4)` lies in `F = f(X...)` where `f(a, b, c, d) = [a, b, c, d]` is a vector function, and `X=IntervalBox(-10..10, 4)` . Using `IntervalArithmetic.jl` package, I tried `Z \in F` and `Z \subseteq F` . Both command give `false` . Could you please let me know how can I check whether `F` contains `Z` or not? The result should be `true` as region `F` contains region `Z`.

Thank you

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<div class="post-metadata">

### Author: ![algunion](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/algunion/32/51630_2.png) [@algunion](https://discourse.julialang.org/u/algunion)
#### Post date: [July 29, 2023, 8:48pm UTC](https://discourse.julialang.org/t/how-to-check-if-region-made-by-one-intervalbox-contains-a-region-made-by-another-intervalbox/102246/2 "2023-07-29T20:48:20Z")

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I think the problem is that `IntervalArithmetic` might not have an internal definition for `\subseteq` (or at least there might be some bug - because calling `methods(⊆)` outputs methods for `issubset`). This might warrant deeper investigation (I suggest also checking the [issues](https://github.com/JuliaIntervals/IntervalArithmetic.jl/issues) section and potentially reporting a new issue).

However, `\subset` is doing the job. Both the following are evaluated as `true` in the context stated by your MWE:

```julia
Z ⊂ X
X ⊃ Z

# alternatively, you can use:
issubset(Z, X) # true

```