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Theorems · Theorem · general topology

Filter.IsBasis.inter

∀ {α : Type u_1} {ι : Sort u_4} {p : ι → Prop} {s : ι → Set α},
  Filter.IsBasis p s → ∀ {i j : ι}, p i → p j → ∃ k, p k ∧ s k ⊆ s i ∩ s j

s is directed downwards on i such that p i.

Defined in
Mathlib.Order.Filter.Bases.Basic
Cited by
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Foundations
Depth 6 from the axioms · uses no axioms

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  • Setstatement and proof · cited by 53,352
  • Filter.IsBasisstatement and proof · cited by 14

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