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Theorems · Theorem · general topology

Filter.eventually_const

∀ {α : Type u} {f : Filter α} [t : f.NeBot] {p : Prop}, (∀ᶠ (x : α) in f, p) ↔ p
Defined in
Mathlib.Order.Filter.Basic
Cited by
8 results in Mathlib
Foundations
Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Filter.NeBot
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LowerSemicontinuousOn.exists_isMinOn · cited by 6LowerSemicontinuousOn.exi…Filter.Germ.liftRel_const_iff · cited by 2Germ.liftRel_const_iffhasFDerivAt_of_tendstoUniformlyOnFilter · cited by 2hasFDerivAt_of_tendstoUni…IsCompactOperator.antilipschitz_of_not_hasEigenvalue · cited by 1IsCompactOperator.antilip…difference_quotients_converge_uniformly · cited by 1difference_quotients_conv…Filter.const_eventuallyEq' · cited by 1Filter.const_eventuallyEq'ArithmeticFunction.isMultiplicative_eulerProduct · cited by 0ArithmeticFunction.isMult…Filter.Germ.liftPred_const_iff · cited by 0Germ.liftPred_const_iffFilter · cited by 8121FilterFilter.Eventually · cited by 3134Filter.EventuallyFilter.NeBot · cited by 853Filter.NeBotFilter.NeBot.ne · cited by 17NeBot.neFilter.eventually_constCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by8

Results whose statement or proof uses this declaration.