[Merged by Bors] - feat(topology/algebra/ordered/basic): sequences tending to Inf/Sup #8524
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sgouezel
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gebner
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Thanks! It's a bit embarrassing that we had a version of this in the tutorials but not in mathlib. I wasn't even able to find the easy directions (if x is an upper bound of s and there is a sequence in s convering to x then is_lub s x). Do you mind adding this while you have the relevant minimal assumptions in mind?
PatrickMassot
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I have added the fact that, if an upper bound belongs to the closure, then it is a lub, and taken all your comments into account (and moved everything to a better place in the file). |
sgouezel
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bors merge |
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…8524) We show that there exist monotone sequences tending to the Inf/Sup of a set in a conditionally complete linear order, as well as several related lemmas expressed in terms of `is_lub` and `is_glb`.
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We show that there exist monotone sequences tending to the Inf/Sup of a set in a conditionally complete linear order, as well as several related lemmas expressed in terms of
is_lubandis_glb.This is a common generalization of lemmas that showed up both in #8388 and #8266