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Theorems · Theorem · general topology

Filter.mem_vadd_filter

∀ {α : Type u_2} {β : Type u_3} [inst : VAdd α β] {f : Filter β} {s : Set β} {a : α},
  s ∈ a +ᵥ f ↔ (fun x => a +ᵥ x) ⁻¹' s ∈ f
Defined in
Mathlib.Order.Filter.Pointwise
Cited by
1 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
VAdd

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

Cites5

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

  • Setstatement and proof · cited by 53,352
  • Filterstatement and proof · cited by 8,121
  • Set.preimagestatement · cited by 4,946
  • HVAdd.hVAddstatement · cited by 1,820
  • VAddstatement and proof · cited by 616

Cited by1

Results whose statement or proof uses this declaration.