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Theorems · Theorem · general topology

Filter.pi_le_pi

∀ {ι : Type u_1} {α : ι → Type u_2} {f₁ f₂ : (i : ι) → Filter (α i)} [∀ (i : ι), (f₁ i).NeBot],
  Filter.pi f₁ ≤ Filter.pi f₂ ↔ ∀ (i : ι), f₁ i ≤ f₂ i
Defined in
Mathlib.Order.Filter.Pi
Cited by
1 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Filter.NeBot
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Around this declaration

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

Filter.pi_inj · cited by 0Filter.pi_injFilter · cited by 8121FilterFilter.NeBot · cited by 853Filter.NeBotFilter.Tendsto.mono_left · cited by 125Tendsto.mono_leftFilter.pi · cited by 48Filter.piFilter.tendsto_eval_pi · cited by 4Filter.tendsto_eval_piFilter.map_eval_pi · cited by 2Filter.map_eval_piFilter.pi_mono · cited by 2Filter.pi_monoFilter.pi_le_piCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.