Theorems · Theorem · general topology
Filter.coprod_inf_prod_le
∀ {α : Type u_1} {β : Type u_2} (f₁ f₂ : Filter α) (g₁ g₂ : Filter β), f₁.coprod g₁ ⊓ f₂ ×ˢ g₂ ≤ f₁ ×ˢ g₂ ⊔ f₂ ×ˢ g₁- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- SProd.sprodstatement and proof · cited by 1,750
- le_rflproof · cited by 1,558
- inf_le_leftproof · cited by 286
- inf_of_le_rightproof · cited by 128
- sup_le_supproof · cited by 48
- inf_sup_rightproof · cited by 26
- Filter.coprodstatement · cited by 23
- Filter.prod_monoproof · cited by 14
- Filter.prod_inf_prodproof · cited by 6
- Filter.coprod_eq_prod_top_sup_top_prodproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- tendsto_mul_coprod_nhds_zero_inf_of_disjoint_cocompactproof · cited by 1