Theorems · Theorem · combinatorics
Nat.choose_eq_zero_of_lt
∀ {n k : ℕ}, n < k → n.choose k = 0- Defined in
- Mathlib.Data.Nat.Choose.Basic
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.choosestatement · cited by 494
Cited by35
Results whose statement or proof uses this declaration.
- Nat.descFactorial_eq_factorial_mul_chooseproof · cited by 12
- Nat.choose_succ_selfproof · cited by 11
- Nat.choose_le_middleproof · cited by 7
- Polynomial.hasseDeriv_monomialproof · cited by 5
- Nat.choose_eq_zero_iffproof · cited by 4
- Nat.choose_mul_succ_eqproof · cited by 4
- Multiset.powersetCard_eq_emptyproof · cited by 4
- Polynomial.taylor_coeffproof · cited by 4
- Polynomial.hasseDeriv_coeffproof · cited by 3
- Nat.factorization_choose_le_logproof · cited by 3
- Nat.Prime.dvd_choose_powproof · cited by 3
- Polynomial.norm_coeff_le_choose_mul_mahlerMeasureproof · cited by 3