Theorems · Theorem · general topology
Filter.prod_inj
∀ {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
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.NeBotFilter.NeBot
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Cites8
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 and proof · cited by 1,750
- Filter.NeBotstatement and proof · cited by 853
- Eq.leproof · cited by 605
- LE.le.antisymmproof · cited by 507
- Eq.geproof · cited by 375
- Filter.neBot_of_leproof · cited by 5
- Filter.prod_le_prodproof · cited by 2
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