[Merged by Bors] - feat(order/filter/ultrafilter): Add variant of exists_ultrafilter.
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Co-authored-by: Patrick Massot <patrickmassot@free.fr>
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…4436) The lemma `exists_ultrafilter` tells us that any proper filter can be extended to an ultrafilter (using Zorn's lemma). This PR adds a variant, called `exists_ultrafilter_of_finite_inter_nonempty` which says that any collection of sets `S` can be extended to an ultrafilter whenever it satisfies the property that the intersection of any finite subcollection `T` is nonempty. Co-authored-by: Adam Topaz <adamtopaz@users.noreply.github.com>
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exists_ultrafilter.exists_ultrafilter.
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…4436) The lemma `exists_ultrafilter` tells us that any proper filter can be extended to an ultrafilter (using Zorn's lemma). This PR adds a variant, called `exists_ultrafilter_of_finite_inter_nonempty` which says that any collection of sets `S` can be extended to an ultrafilter whenever it satisfies the property that the intersection of any finite subcollection `T` is nonempty. Co-authored-by: Adam Topaz <adamtopaz@users.noreply.github.com>
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The lemma
exists_ultrafiltertells us that any proper filter can be extended to an ultrafilter (using Zorn's lemma). This PR adds a variant, calledexists_ultrafilter_of_finite_inter_nonemptywhich says that any collection of setsScan be extended to an ultrafilter whenever it satisfies the property that the intersection of any finite subcollectionTis nonempty.