Theorems · Theorem · number theory
Nat.factorization_choose_eq_zero_of_lt
∀ {p n k : ℕ}, n < p → (n.choose k).factorization p = 0- Defined in
- Mathlib.Data.Nat.Choose.Factorization
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsuppstatement and proof · cited by 5,255
- Nat.factorialproof · cited by 616
- Nat.choosestatement · cited by 494
- Nat.factorizationstatement and proof · cited by 215
- zero_tsubproof · cited by 100
- Nat.choose_eq_zero_of_ltproof · cited by 35
- Nat.factorization_zeroproof · cited by 32
- Pi.sub_applyproof · cited by 24
- Nat.choose_eq_factorial_div_factorialproof · cited by 8
- Nat.factorization_divproof · cited by 7
- Nat.factorial_mul_factorial_dvd_factorialproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Nat.factorization_centralBinom_eq_zero_of_two_mul_ltproof · cited by 1
- Nat.prod_pow_factorization_chooseproof · cited by 1