Theorems · Theorem · combinatorics
Set.powersetCard.nontrivial
∀ {α : Type u_1} {n : ℕ}, 0 < n → ↑n < ENat.card α → Nontrivial ↑(Set.powersetCard α n)If 0 < n < ENat.card α, then powersetCard α n is nontrivial.
- Defined in
- Mathlib.Data.Set.PowersetCard
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypeproof · cited by 7,736
- Set.Elemstatement · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Nontrivialstatement · cited by 2,416
- Fintype.cardproof · cited by 1,386
- Nat.cardproof · cited by 844
- Nat.chooseproof · cited by 494
- Infiniteproof · cited by 352
- Nat.card_eq_fintype_cardproof · cited by 200
- lt_transproof · cited by 165
- Set.powersetCardstatement and proof · cited by 100
Cited by2
Results whose statement or proof uses this declaration.
- Set.powersetCard.isPreprimitive_alternatingGroupproof · cited by 2
- Set.powersetCard.nontrivial'proof · cited by 1