# [tlaplus] Removing "equivalents" from a set

Hello. I have a small problem that I haven't been able to solve:

What I'm trying to achieve is given a set of numbers, I want to partition it into smaller sets(in this case with size 2), and eliminate equivalent partitions to save resources.
6 hours later, I have arrived at this result, which is almost what I want:
`s == { {{1}},     {{2}},     {{3}},     {{4}},     {{1, 2}},     {{1, 3}},     {{1, 4}},     {{2, 3}},     {{2, 4}},     {{3, 4}},     {{1}, {2, 3}},     {{1}, {2, 4}},     {{1}, {3, 4}},     {{2}, {1, 3}},     {{2}, {1, 4}},     {{2}, {3, 4}},     {{3}, {1, 2}},     {{3}, {1, 4}},     {{3}, {2, 4}},     {{4}, {1, 2}},     {{4}, {1, 3}},     {{4}, {2, 3}},     {{1, 2}, {3, 4}},     {{1, 3}, {2, 4}},     {{1, 4}, {2, 3}} }`
What I am trying to do is to remove elements of this set, if the element's UNION is already contained in the set, giving me the following set:
`{ {{1}},     {{2}},     {{3}},     {{4}},     {{1, 2}},     {{1, 3}},     {{1, 4}},     {{2, 3}},     {{2, 4}},     {{3, 4}},     {{1}, {2, 3}},     {{1}, {2, 4}},     {{1}, {3, 4}},     {{2}, {3, 4}},     {{1, 2}, {3, 4}} }`

How could this be done? I have not found any way asserting that a predicate is true for every pair of elements in a set.

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