Theorems · Theorem · order theory
Set.Infinite.exists_subset_card_eq
∀ {α : Type u} {s : Set α}, s.Infinite → ∀ (n : ℕ), ∃ t, ↑t ⊆ s ∧ t.card = n- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement · cited by 8,199
- Set.imageproof · cited by 5,609
- Finset.cardstatement · cited by 2,327
- Finset.rangeproof · cited by 1,341
- Set.Iioproof · cited by 1,166
- Finset.mapproof · cited by 747
- Set.Infinitestatement and proof · cited by 263
- Function.Embedding.subtypeproof · cited by 128
- Finset.coe_mapproof · cited by 114
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.count_apply_infiniteproof · cited by 5
- Set.Infinite.exists_subset_ncard_eqproof · cited by 1
- Function.locallyFinsuppWithin.finite_support_of_logCounting_isBigO_logproof · cited by 1
- Set.infinite_iff_tendsto_sum_indicator_atTopproof · cited by 1