Theorems · Theorem · general topology
Filter.prod_inf_prod
∀ {α : Type u_1} {β : Type u_2} {f₁ f₂ : Filter α} {g₁ g₂ : Filter β}, f₁ ×ˢ g₁ ⊓ f₂ ×ˢ g₂ = (f₁ ⊓ f₂) ×ˢ (g₁ ⊓ g₂)- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 63 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.
- Filterstatement and proof · cited by 8,121
- SProd.sprodstatement · cited by 1,750
- Filter.comapproof · cited by 546
- inf_commproof · cited by 139
- inf_assocproof · cited by 53
- Filter.comap_infproof · cited by 33
- inf_left_commproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- Filter.coprod_inf_prod_leproof · cited by 1
- BoxIntegral.Integrable.cauchy_map_integralSum_toFilteriUnionproof · cited by 1
- Filter.disjoint_prodproof · cited by 0
- Filter.tendstoIxxClass_infproof · cited by 0
- Filter.prod_infproof · cited by 0
- Filter.inf_prodproof · cited by 0