Theorems · Theorem · general topology
Filter.OrderBot.atBot_eq
∀ (α : Type u_6) [inst : PartialOrder α] [inst_1 : OrderBot α], Filter.atBot = pure ⊥
- Defined in
- Mathlib.Order.Filter.AtTopBot.Tendsto
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- Filter.principalproof · cited by 740
- Filter.atBotstatement · cited by 512
- Filter.principal_singletonproof · cited by 31
- isBot_botproof · cited by 9
- Set.Iic_botproof · cited by 7
- IsBot.atBot_eqproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Filter.atBot_eq_pure_of_isBotproof · cited by 2
- ProbabilityTheory.Kernel.trajContent_tendsto_zeroproof · cited by 1
- Filter.tendsto_atBot_pureproof · cited by 0
- MeasureTheory.tendsto_of_lintegral_tendsto_of_antitoneproof · cited by 0