Mathlib Map

Theorems · Theorem · general topology

Filter.inter_sets

∀ {α : Type u_1} (self : Filter α) {x y : Set α}, x ∈ self.sets → y ∈ self.sets → x ∩ y ∈ self.sets

If two sets belong to a filter, then their intersection belongs to the filter as well.

Defined in
Mathlib.Order.Filter.Defs
Cited by
4 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms

Around this declaration

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Cites3

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

  • Setstatement · cited by 53,352
  • Filterstatement and proof · cited by 8,121
  • Filter.setsstatement · cited by 56

Cited by4

Results whose statement or proof uses this declaration.