Theorems · Theorem · combinatorics
Nat.choose_eq_zero_iff
∀ {n k : ℕ}, n.choose k = 0 ↔ n < k- Defined in
- Mathlib.Data.Nat.Choose.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
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.
- Nat.choosestatement and proof · cited by 494
- lt_of_not_geproof · cited by 374
- Nat.choose_eq_zero_of_ltproof · cited by 35
- Eq.not_ltproof · cited by 22
- Nat.choose_posproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- Set.powersetCard.nontrivialproof · cited by 2
- Set.powersetCard.isPretransitive_alternatingGroupproof · cited by 1
- Set.powersetCard.nontrivial_iffproof · cited by 0
- Set.powersetCard.eq_empty_iffproof · cited by 0