Theorems · Theorem · general topology
Filter.eventually_lt_atBot
∀ {α : Type u_3} [inst : Preorder α] [NoBotOrder α] (a : α), ∀ᶠ (x : α) in Filter.atBot, x < a- Defined in
- Mathlib.Order.Filter.AtTopBot.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
- Assumes
- PreorderNoBotOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Filter.Eventuallystatement · cited by 3,134
- Filter.atBotstatement · cited by 512
- NoBotOrderstatement and proof · cited by 43
- Filter.Iio_mem_atBotproof · cited by 7
Cited by8
Results whose statement or proof uses this declaration.
- Filter.eventually_ne_atBotproof · cited by 4
- discrim_le_zeroproof · cited by 3
- cexp_neg_quadratic_isLittleO_abs_rpow_cocompactproof · cited by 2
- Filter.Tendsto.eventually_lt_atBotproof · cited by 2
- Finset.tendsto_Ioc_atBot_prod_atTopproof · cited by 1
- Finset.tendsto_Ioo_atBot_prod_atTopproof · cited by 1
- Polynomial.isEquivalent_atBot_divproof · cited by 1
- pow_div_pow_eventuallyEq_atBotproof · cited by 0