From the link it seems you have proved the result. What about the following what seems to be a counterexample?
(the set of integers), , the set of all infinite sets of integers
Now there is no set that would be minimal in ...
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CSI of Charles University
A counterexample?
From the link it seems you have proved the result. What about the following what seems to be a counterexample?
Now there is no set
that would be minimal in 
...