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[Merged by Bors] - feat(NumberTheory.NumberField.CanonicalEmbedding): add exists_ne_zero_mem_ringOfIntegers_lt #5650

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@xroblot xroblot commented Jul 1, 2023

This PR proves the following result:

theorem exists_ne_zero_mem_ringOfIntegers_lt (h : minkowski_bound K < volume (convex_body_lt K f)) :
     βˆƒ (a : π“ž K), a β‰  0 ∧ βˆ€ w : InfinitePlace K, w a < f w 

where f : InfinitePlace K β†’ ℝβ‰₯0 and convex_body_lt K f is the set of points x such that β€–x wβ€– < f w for all infinite places w. This is a key result in the proof of Dirichlet's unit theorem #5960


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@kim-em kim-em added the blocked-by-other-PR This PR depends on another PR to Mathlib (this label is automatically managed by a bot) label Jul 1, 2023
@xroblot xroblot added the WIP Work in progress label Jul 9, 2023
@xroblot xroblot added the t-number-theory Number theory (also use t-algebra or t-analysis to specialize) label Jul 18, 2023
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot removed the blocked-by-other-PR This PR depends on another PR to Mathlib (this label is automatically managed by a bot) label Sep 16, 2023
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Sep 16, 2023
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Sep 16, 2023
@bors bors bot changed the base branch from master to ScottCarnahan/BinomialRing2 September 17, 2023 03:25
@kim-em kim-em changed the base branch from ScottCarnahan/BinomialRing2 to master September 17, 2023 12:16
@jcommelin jcommelin added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review labels Sep 18, 2023
@xroblot xroblot added awaiting-review and removed awaiting-author A reviewer has asked the author a question or requested changes labels Sep 19, 2023
@jcommelin jcommelin changed the title feat(NumberTheory.NumberField.CanonicalEmbedding): add exists_ne_zero_mem_ring_of_integers_lt feat(NumberTheory.NumberField.CanonicalEmbedding): add exists_ne_zero_mem_ringOfIntegers_lt Sep 19, 2023
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I think this is looking pretty good now. If you fix the two naming issues that I pointed out above, please kick this on the bors queue.

bors d+

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bors bot commented Sep 19, 2023

✌️ xroblot can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

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xroblot commented Sep 20, 2023

bors r+

bors bot pushed a commit that referenced this pull request Sep 20, 2023
…_mem_ringOfIntegers_lt (#5650)

This PR proves the following result: 
```lean
theorem exists_ne_zero_mem_ringOfIntegers_lt (h : minkowski_bound K < volume (convex_body_lt K f)) :
     βˆƒ (a : π“ž K), a β‰  0 ∧ βˆ€ w : InfinitePlace K, w a < f w 
```
where `f : InfinitePlace K β†’ ℝβ‰₯0` and `convex_body_lt K f` is the set of points `x` such that `β€–x wβ€– < f w` for all infinite places `w`. This is a key result in the proof of Dirichlet's unit theorem #5960
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Pull request successfully merged into master.

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@bors bors bot changed the title feat(NumberTheory.NumberField.CanonicalEmbedding): add exists_ne_zero_mem_ringOfIntegers_lt [Merged by Bors] - feat(NumberTheory.NumberField.CanonicalEmbedding): add exists_ne_zero_mem_ringOfIntegers_lt Sep 20, 2023
@bors bors bot closed this Sep 20, 2023
@bors bors bot deleted the xfr-canonical_embedding_minkowski branch September 20, 2023 09:59
kodyvajjha pushed a commit that referenced this pull request Sep 22, 2023
…_mem_ringOfIntegers_lt (#5650)

This PR proves the following result: 
```lean
theorem exists_ne_zero_mem_ringOfIntegers_lt (h : minkowski_bound K < volume (convex_body_lt K f)) :
     βˆƒ (a : π“ž K), a β‰  0 ∧ βˆ€ w : InfinitePlace K, w a < f w 
```
where `f : InfinitePlace K β†’ ℝβ‰₯0` and `convex_body_lt K f` is the set of points `x` such that `β€–x wβ€– < f w` for all infinite places `w`. This is a key result in the proof of Dirichlet's unit theorem #5960
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