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Commit 2021-12-30 00:20 ea95523d

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feat(analysis/normed_space/dual): add lemmas, golf (#11132)

  • 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).

Estimated changes

added theorem is_closed_polar
added theorem polar_Union
added theorem polar_antitone
added theorem polar_closure
modified theorem polar_empty
added theorem polar_gc
added theorem polar_union
added theorem polar_univ
added theorem polar_zero