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Theorems · Theorem · general topology

Filter.le_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {f : (i : ι) → Filter (α i)} {g : Filter ((i : ι) → α i)},
  g ≤ Filter.pi f ↔ ∀ (i : ι), Filter.Tendsto (Function.eval i) g (f i)
Defined in
Mathlib.Order.Filter.Pi
Cited by
2 results in Mathlib
Foundations
Depth 67 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.

IsProperMap.pi_map · cited by 0IsProperMap.pi_mapFilter.le_pi_principal · cited by 0Filter.le_pi_principalFilter · cited by 8121FilterFilter.Tendsto · cited by 3814Filter.TendstoFunction.eval · cited by 140Function.evalFilter.pi · cited by 48Filter.piFilter.tendsto_pi · cited by 7Filter.tendsto_piFilter.le_piCITED BYCITES

Cites5

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Cited by2

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