Theorems · Theorem · number theory
Nat.Prime.emultiplicity_le_emultiplicity_choose_add
∀ {p : ℕ}, Nat.Prime p → ∀ (n k : ℕ), emultiplicity p n ≤ emultiplicity p (n.choose k) + emultiplicity p kA lower bound on the multiplicity of p in choose n k.
- Defined in
- Mathlib.Data.Nat.Multiplicity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- Nat.Primestatement and proof · cited by 2,059
- Nat.choosestatement and proof · cited by 494
- emultiplicitystatement and proof · cited by 156
- dvd_mul_rightproof · cited by 89
- top_addproof · cited by 55
- Nat.choose_zero_rightproof · cited by 55
- add_topproof · cited by 49
- emultiplicity_zeroproof · cited by 10
- Nat.add_one_mul_choose_eqproof · cited by 7
- Nat.Prime.emultiplicity_mulproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicityproof · cited by 2