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Theorems · Theorem · general topology

Filter.pi_mono

∀ {ι : Type u_1} {α : ι → Type u_2} {f₁ f₂ : (i : ι) → Filter (α i)},
  (∀ (i : ι), f₁ i ≤ f₂ i) → Filter.pi f₁ ≤ Filter.pi f₂
Defined in
Mathlib.Order.Filter.Pi
Cited by
2 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.pi_le_pi · cited by 1Filter.pi_le_piIsOpenMap.piMap · cited by 1IsOpenMap.piMapFilter · cited by 8121FilterFilter.pi · cited by 48Filter.piiInf_mono · cited by 29iInf_monoFilter.comap_mono · cited by 16Filter.comap_monoFilter.pi_monoCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.