[Merged by Bors] - feat(combinatorics/additive/salem_spencer): The sphere does not contain arithmetic progressions #13259
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…in arithmetic progressions (#13259) Prove that the frontier of a strictly convex closed set is Salem-Spencer. For this we need * simple lemmas about `same_ray`. This involves renaming `same_ray.exists_right_eq_smul`/`same_ray.exists_left_eq_smul` to `same_ray.exists_nonneg_left`/`same_ray.exists_nonneg_right`. * that the norm in a real normed space is injective on rays. * that the midpoint of two points of equal norm has smaller norm, in a strictly convex space
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…in arithmetic progressions (#13259) Prove that the frontier of a strictly convex closed set is Salem-Spencer. For this we need * simple lemmas about `same_ray`. This involves renaming `same_ray.exists_right_eq_smul`/`same_ray.exists_left_eq_smul` to `same_ray.exists_nonneg_left`/`same_ray.exists_nonneg_right`. * that the norm in a real normed space is injective on rays. * that the midpoint of two points of equal norm has smaller norm, in a strictly convex space
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…in arithmetic progressions (#13259) Prove that the frontier of a strictly convex closed set is Salem-Spencer. For this we need * simple lemmas about `same_ray`. This involves renaming `same_ray.exists_right_eq_smul`/`same_ray.exists_left_eq_smul` to `same_ray.exists_nonneg_left`/`same_ray.exists_nonneg_right`. * that the norm in a real normed space is injective on rays. * that the midpoint of two points of equal norm has smaller norm, in a strictly convex space
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…in arithmetic progressions (#13259) Prove that the frontier of a strictly convex closed set is Salem-Spencer. For this we need * simple lemmas about `same_ray`. This involves renaming `same_ray.exists_right_eq_smul`/`same_ray.exists_left_eq_smul` to `same_ray.exists_nonneg_left`/`same_ray.exists_nonneg_right`. * that the norm in a real normed space is injective on rays. * that the midpoint of two points of equal norm has smaller norm, in a strictly convex space
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Prove that the frontier of a strictly convex closed set is Salem-Spencer. For this we need
same_ray. This involves renamingsame_ray.exists_right_eq_smul/same_ray.exists_left_eq_smultosame_ray.exists_nonneg_left/same_ray.exists_nonneg_right.This is a very nice stress test of the library, because the end result is combinatorics but everything that leads to it is functional analysis.
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