Theorems · Theorem · general topology
Filter.prod_mono
∀ {α : Type u_1} {β : Type u_2} {f₁ f₂ : Filter α} {g₁ g₂ : Filter β}, f₁ ≤ f₂ → g₁ ≤ g₂ → f₁ ×ˢ g₁ ≤ f₂ ×ˢ g₂- Defined in
- Mathlib.Order.Filter.Prod
- Cited by
- 14 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.
Cites4
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
- inf_le_infproof · cited by 54
- Filter.comap_monoproof · cited by 16
Cited by14
Results whose statement or proof uses this declaration.
- Filter.Tendsto.prodMapproof · cited by 38
- HasFDerivWithinAt.monoproof · cited by 32
- exists_fun_of_mem_tangentConeAtproof · cited by 9
- Cauchy.monoproof · cited by 6
- Filter.prod_mono_rightproof · cited by 6
- IsOpenMap.prodMapproof · cited by 6
- Filter.prod_mono_leftproof · cited by 5
- IsCompact.nhdsSet_prod_eq_biSupproof · cited by 3
- Filter.prod_le_prodproof · cited by 2
- Filter.coprod_inf_prod_leproof · cited by 1
- Cauchy.ultrafilter_ofproof · cited by 1
- IsCompact.mem_nhdsSet_prod_of_forallproof · cited by 1