Theorems · Theorem · general topology
Filter.prod_mem_prod
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β} {f : Filter α} {g : Filter β}, s ∈ f → t ∈ g → s ×ˢ t ∈ f ×ˢ g- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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
- SProd.sprodstatement · cited by 1,750
- Filter.preimage_mem_comapproof · cited by 23
- Filter.inter_mem_infproof · cited by 11
Cited by20
Results whose statement or proof uses this declaration.
- Filter.prod_map_map_eqproof · cited by 17
- nhds_le_uniformityproof · cited by 5
- Ultrafilter.cauchy_of_totallyBounded'proof · cited by 4
- isLocallyInjective_iff_isOpen_diagonalproof · cited by 3
- Metric.eventually_nhds_zero_forall_closedEBall_subsetproof · cited by 2
- nhdsWithin_prodproof · cited by 2
- Filter.prod_mem_prod_iffproof · cited by 2
- Frullani.tendsto_intervalIntegralproof · cited by 1
- IsSeqCompact.isCompleteproof · cited by 1
- IsDenseInducing.extend_Z_bilinproof · cited by 1
- ContinuousSMul.of_basis_zeroproof · cited by 1
- MeasureTheory.hasFDerivAt_convolution_right_with_paramproof · cited by 1