[Merged by Bors] - feat(analysis/normed_space/dual): add lemmas, golf #11132
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* add `polar_univ`, `is_closed_polar`, `polar_gc`, `polar_Union`, `polar_union`, `polar_antitone`, `polar_zero`, `polar_closure`; * extract `polar_ball_subset_closed_ball_div` and `closed_ball_inv_subset_polar_closed_ball` out of the proofs of `polar_closed_ball` and `polar_bounded_of_nhds_zero`; * rename `polar_bounded_of_nhds_zero` to `bounded_polar_of_mem_nhds_zero`, use `metric.bounded`; * use `r⁻¹` instead of `1 / r` in `polar_closed_ball`. This is the simp normal form (though we might want to change this in the future).
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This PR/issue depends on:
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| variable (E) | ||
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| lemma polar_gc : | ||
| galois_connection (order_dual.to_dual ∘ polar 𝕜) |
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I think this order_dual.to_dual ∘ is worth a docstring comment.
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Dec 30, 2021
Co-authored-by: Patrick Massot <patrickmassot@free.fr>
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* add `polar_univ`, `is_closed_polar`, `polar_gc`, `polar_Union`, `polar_union`, `polar_antitone`, `polar_zero`, `polar_closure`; * extract `polar_ball_subset_closed_ball_div` and `closed_ball_inv_subset_polar_closed_ball` out of the proofs of `polar_closed_ball` and `polar_bounded_of_nhds_zero`; * rename `polar_bounded_of_nhds_zero` to `bounded_polar_of_mem_nhds_zero`, use `metric.bounded`; * use `r⁻¹` instead of `1 / r` in `polar_closed_ball`. This is the simp normal form (though we might want to change this in the future).
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* add `polar_univ`, `is_closed_polar`, `polar_gc`, `polar_Union`, `polar_union`, `polar_antitone`, `polar_zero`, `polar_closure`; * extract `polar_ball_subset_closed_ball_div` and `closed_ball_inv_subset_polar_closed_ball` out of the proofs of `polar_closed_ball` and `polar_bounded_of_nhds_zero`; * rename `polar_bounded_of_nhds_zero` to `bounded_polar_of_mem_nhds_zero`, use `metric.bounded`; * use `r⁻¹` instead of `1 / r` in `polar_closed_ball`. This is the simp normal form (though we might want to change this in the future).
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add
polar_univ,is_closed_polar,polar_gc,polar_Union,polar_union,polar_antitone,polar_zero,polar_closure;extract
polar_ball_subset_closed_ball_divandclosed_ball_inv_subset_polar_closed_ballout of the proofs ofpolar_closed_ballandpolar_bounded_of_nhds_zero;rename
polar_bounded_of_nhds_zerotobounded_polar_of_mem_nhds_zero, usemetric.bounded;use
r⁻¹instead of1 / rinpolar_closed_ball. This is thesimp normal form (though we might want to change this in the future).
a / a ≤ 1#11118