Theorems · Theorem · general topology
Filter.prod_principal_principal
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β},
Filter.principal s ×ˢ Filter.principal t = Filter.principal (s ×ˢ t)- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 8,121
- Set.preimageproof · cited by 4,946
- SProd.sprodstatement and proof · cited by 1,750
- Filter.principalstatement and proof · cited by 740
- Filter.comap_principalproof · cited by 47
- Filter.inf_principalproof · cited by 29
Cited by9
Results whose statement or proof uses this declaration.
- Filter.prod_atTop_atTop_eqproof · cited by 20
- nhdsWithin_prod_eqproof · cited by 7
- IsCompact.nhdsSetWithin_prod_eqproof · cited by 3
- TendstoUniformlyOn.prodMapproof · cited by 2
- Filter.prod_lift'_lift'proof · cited by 1
- BoxIntegral.Integrable.cauchy_map_integralSum_toFilteriUnionproof · cited by 1
- Filter.frequently_prod_andproof · cited by 0
- Filter.tendstoIxxClass_principalproof · cited by 0
- nhdsSetWithin_prod_leproof · cited by 0