Theorems · Theorem · combinatorics
Set.powersetCard.exists_mem_notMem
∀ {α : Type u_1} {n : ℕ}, 1 ≤ n → ↑n < ENat.card α → ∀ {a b : α}, a ≠ b → ∃ s, a ∈ s ∧ b ∉ s- Defined in
- Mathlib.Data.Set.PowersetCard
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetstatement · cited by 13,712
- Set.Elemstatement · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Compl.complproof · cited by 2,925
- Set.Finiteproof · cited by 1,814
- add_commproof · cited by 1,535
- Set.Finite.toFinsetproof · cited by 351
- Set.encardproof · cited by 327
- Set.powersetCardstatement · cited by 100
- ENat.cardstatement and proof · cited by 89
- Set.encard_singletonproof · cited by 26
Cited by2
Results whose statement or proof uses this declaration.
- Set.powersetCard.addAction_faithfulproof · cited by 1
- Set.powersetCard.mulAction_faithfulproof · cited by 1