Theorems · Theorem · general topology
Filter.mem_prod_self_iff
∀ {α : Type u_1} {la : Filter α} {s : Set (α × α)}, s ∈ la ×ˢ la ↔ ∃ t ∈ la, t ×ˢ t ⊆ s- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SProd.sprodstatement · cited by 1,750
- Filter.HasBasis.mem_iffproof · cited by 193
- Filter.basis_setsproof · cited by 105
- Filter.HasBasis.prod_selfproof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- Filter.mem_prod_same_iffproof · cited by 5
- Filter.eventually_prod_self_iffproof · cited by 2
- not_integrableOn_of_tendsto_norm_atTop_of_deriv_isBigO_filter_auxproof · cited by 1
- exists_nhds_half_negproof · cited by 1