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Theorems · Theorem · general topology

Filter.eventuallyConst_iff_exists_eventuallyEq

∀ {α : Type u_1} {β : Type u_2} {l : Filter α} {f : α → β} [Nonempty β],
  Filter.EventuallyConst f l ↔ ∃ c, f =ᶠ[l] fun x => c
Defined in
Mathlib.Order.Filter.EventuallyConst
Cited by
3 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty
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Around this declaration

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

circleMap_preimage_codiscrete · cited by 3circleMap_preimage_codisc…AnalyticAt.preimage_of_nhdsNE · cited by 2AnalyticAt.preimage_of_nh…Filter.EventuallyConst.eventuallyEq_const · cited by 0EventuallyConst.eventuall…Filter · cited by 8121FilterFilter.EventuallyEq · cited by 1912Filter.EventuallyEqFilter.EventuallyConst · cited by 93Filter.EventuallyConstFilter.subsingleton_iff_exists_singleton_mem · cited by 1Filter.subsingleton_iff_e…Filter.eventuallyConst_iff_ex…CITED BYCITES

Cites4

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Cited by3

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