Theorems · Theorem · logic and foundations
Set.exists_subset_card_eq
∀ {α : Type u_1} {s : Set α} {n : ℕ}, n ≤ s.ncard → ∃ t ⊆ s, t.ncard = nWe can shrink a set to any smaller size.
- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.ncardstatement and proof · cited by 344
- Set.empty_subsetproof · cited by 70
- Set.ncard_emptyproof · cited by 14
- Set.exists_subsuperset_card_eqproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsMultiplyPretransitive.alternatingGroup_leproof · cited by 1
- SimpleGraph.Subgraph.IsMatching.exists_of_universalVertsproof · cited by 0