Theorems · Theorem · order theory
Set.Iic_bot
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : OrderBot α], Set.Iic ⊥ = {⊥}- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement · cited by 4,720
- Set.Iicstatement · cited by 1,111
- OrderBotstatement and proof · cited by 1,055
- isMin_botproof · cited by 15
- IsMin.Iic_eqproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Filter.OrderBot.atBot_eqproof · cited by 4
- partialSups_botproof · cited by 2
- Subgroup.upperCentralSeries.StrictMonoOnproof · cited by 2
- SummationFilter.conditional_filter_eq_map_Iicproof · cited by 1
- AddSubgroup.upperCentralSeries.StrictMonoOnproof · cited by 1
- Filter.nhds_botproof · cited by 0
- OrderBot.lowerBounds_univproof · cited by 0