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[Merged by Bors] - feat(NumberTheory.NumberField.CanonicalEmbedding): add exists_ne_zero_mem_ringOfIntegers_lt #5650
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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 r+ |
β¦_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)) : β (a : π K), a β 0 β§ β w : InfinitePlace K, w a < f w ``` where `f : InfinitePlace K β ββ₯0` and `convex_body_lt K f` is the set of points `x` such that `βx 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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β¦_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)) : β (a : π K), a β 0 β§ β w : InfinitePlace K, w a < f w ``` where `f : InfinitePlace K β ββ₯0` and `convex_body_lt K f` is the set of points `x` such that `βx wβ < f w` for all infinite places `w`. This is a key result in the proof of Dirichlet's unit theorem #5960
This PR proves the following result:
where
f : InfinitePlace K β ββ₯0
andconvex_body_lt K f
is the set of pointsx
such thatβx wβ < f w
for all infinite placesw
. This is a key result in the proof of Dirichlet's unit theorem #5960