Theorems · Theorem · general topology
Filter.map_card_atTop
∀ {α : Type u_3} [Infinite α], Filter.map Finset.card Filter.atTop = Filter.atTopThe pushforward of atTop on Finset α along Finset.card is atTop on ℕ, when α is
infinite.
- Defined in
- Mathlib.Order.Filter.AtTopBot.Finset
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Filter.atTopstatement and proof · cited by 2,405
- Finset.cardstatement and proof · cited by 2,327
- Set.extproof · cited by 2,266
- iInfproof · cited by 1,690
- Filter.mapstatement · cited by 819
- Filter.principalproof · cited by 740
- Infinitestatement and proof · cited by 352
- Finset.card_le_cardproof · cited by 118
Cited by2
Results whose statement or proof uses this declaration.
- Filter.tendsto_card_atTop_atTopproof · cited by 0
- Filter.tendsto_comp_card_atTop_iffproof · cited by 0