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Commit 2022-05-22 04:22 a8a211f2

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feat(order/lattice): add left_lt_inf etc (#14152)

  • add left_lt_sup, right_lt_sup, left_or_right_lt_sup, and their inf counterparts;
  • generalize is_top_or_exists_gt and is_bot_or_exists_lt to directed orders, replacing forall_le_or_exists_lt_inf and forall_le_or_exists_lt_sup;
  • generalize exists_lt_of_sup and exists_lt_of_inf to directed orders, rename them to exists_lt_of_directed_le and exists_lt_of_directed_ge.

Estimated changes

deleted theorem exists_lt_of_inf
deleted theorem exists_lt_of_sup
added theorem inf_lt_left
added theorem inf_lt_left_or_right
added theorem inf_lt_right
added theorem left_lt_sup
added theorem left_or_right_lt_sup
added theorem right_lt_sup