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Theorems · Theorem · general topology

Filter.mem_iSup

∀ {α : Type u} {ι : Sort x} {x : Set α} {f : ι → Filter α}, x ∈ iSup f ↔ ∀ (i : ι), x ∈ f i
Defined in
Mathlib.Order.Filter.Basic
Cited by
3 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

MeasureTheory.Measure.ae_sum_eq · cited by 2Measure.ae_sum_eqFilter.ker_iSup · cited by 2Filter.ker_iSupFilter.eventually_iSup · cited by 1Filter.eventually_iSupSet · cited by 53352SetFilter · cited by 8121FilteriSup · cited by 2415iSupFilter.sets · cited by 56Filter.setsFilter.iSup_sets_eq · cited by 1Filter.iSup_sets_eqFilter.mem_iSupCITED BYCITES

Cites5

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Cited by3

Results whose statement or proof uses this declaration.