Commit 2025-12-18 23:55 29f37a66

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chore(Order/WithBot): add to_dual attributes (part 2) (#32626) Some design considerations:

  • The and < instances on WithBot and WithTop are were deliberately made def-eq. I've not changed this, which results in some awkward code before we develop the API to hide this.
  • There was some major disparity in the unbot and untop API. I had to add a bunch of lemmas to amend it.
  • I reordered a few theorems to avoid having to constantly open and close the WithBot namespace.

Estimated changes

modified theorem WithBot.bot_lt_coe
modified theorem WithBot.coe_le_coe
modified theorem WithBot.coe_lt_coe
modified theorem WithBot.le_def
added theorem WithBot.le_unbotA
added theorem WithBot.le_unbotA_iff
added theorem WithBot.le_unbotD
added theorem WithBot.le_unbotD_iff
modified theorem WithBot.le_unbot_iff
modified theorem WithBot.lt_def
added theorem WithBot.lt_unbotA_iff
added theorem WithBot.lt_unbotD_iff
modified theorem WithBot.lt_unbot_iff
added theorem WithBot.unbotA_le_iff
added theorem WithBot.unbotA_lt_iff
added theorem WithBot.unbotA_mono
added theorem WithBot.unbotD_mono
modified theorem WithBot.unbot_le_iff
deleted theorem WithBot.unbot_le_unbot
deleted theorem WithBot.unbot_lt_unbot
deleted theorem WithTop.coe_le_coe
deleted theorem WithTop.coe_le_iff
deleted theorem WithTop.coe_lt_coe
deleted theorem WithTop.coe_lt_iff
deleted theorem WithTop.coe_lt_top
deleted theorem WithTop.coe_top_lt
deleted theorem WithTop.coe_untopD_le
deleted theorem WithTop.le_coe
deleted theorem WithTop.le_coe_iff
added theorem WithTop.le_def'
modified theorem WithTop.le_def
deleted theorem WithTop.le_iff_forall
deleted theorem WithTop.le_untopA_iff
deleted theorem WithTop.le_untopD_iff
deleted theorem WithTop.le_untop_iff
added theorem WithTop.lt_def'
modified theorem WithTop.lt_def
deleted theorem WithTop.lt_iff_exists
deleted theorem WithTop.lt_iff_exists_coe
deleted theorem WithTop.lt_untopA_iff
deleted theorem WithTop.lt_untopD_iff
deleted theorem WithTop.lt_untop_iff
deleted theorem WithTop.map_le_iff
deleted theorem WithTop.not_top_le_coe
deleted theorem WithTop.untopA_le
deleted theorem WithTop.untopA_le_iff
deleted theorem WithTop.untopA_lt_iff
deleted theorem WithTop.untopA_mono
deleted theorem WithTop.untopD_le
deleted theorem WithTop.untopD_le_iff
deleted theorem WithTop.untopD_lt_iff
deleted theorem WithTop.untopD_mono
deleted theorem WithTop.untop_le_iff
deleted theorem WithTop.untop_lt_iff
deleted theorem WithTop.untop_mono