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[Merged by Bors] - chore(topology/algebra/ordered): fix assumptions in some lemmas #3629

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[Merged by Bors] - chore(topology/algebra/ordered): fix assumptions in some lemmas #3629

wants to merge 1 commit into from

Commits on Jul 30, 2020

  1. chore(topology/algebra/ordered): fix assumptions in some lemmas 

    * Some `nhds_within_I??_eq_nhds_within_I??` lemmas assumed strict
  inequalities when this was not needed.
* Remove TFAEs that only stated equality of three `nhds_within`s.
  Prove equality of `nhds_within`s instead.
* Genralize `I??_mem_nhds_within_I??` to `order_closed_topology`.
    @urkud
    urkud committed Jul 30, 2020
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