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Theorems · Theorem · general topology

Filter.prod_le_prod

∀ {α : Type u_1} {β : Type u_2} {f₁ f₂ : Filter α} {g₁ g₂ : Filter β} [f₁.NeBot] [g₁.NeBot],
  f₁ ×ˢ g₁ ≤ f₂ ×ˢ g₂ ↔ f₁ ≤ f₂ ∧ g₁ ≤ g₂
Defined in
Mathlib.Order.Filter.Prod
Cited by
2 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Filter.NeBotFilter.NeBot
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Around this declaration

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

CauchySeq.comp_tendsto · cited by 3CauchySeq.comp_tendstoFilter.prod_inj · cited by 0Filter.prod_injFilter · cited by 8121FilterSProd.sprod · cited by 1750SProd.sprodFilter.NeBot · cited by 853Filter.NeBotFilter.Tendsto.mono_left · cited by 125Tendsto.mono_leftFilter.tendsto_snd · cited by 30Filter.tendsto_sndFilter.tendsto_fst · cited by 26Filter.tendsto_fstFilter.prod_mono · cited by 14Filter.prod_monoFilter.map_fst_prod · cited by 5Filter.map_fst_prodFilter.map_snd_prod · cited by 5Filter.map_snd_prodFilter.prod_le_prodCITED BYCITES

Cites9

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Cited by2

Results whose statement or proof uses this declaration.