Theorems · Theorem · number theory
sum_bernoulli
∀ (n : ℕ), ∑ k ∈ Finset.range n, ↑(n.choose k) * bernoulli k = if n = 1 then 1 else 0
- Defined in
- Mathlib.NumberTheory.Bernoulli
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 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.
- Finsetproof · cited by 13,712
- AddCommMonoidproof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- Finset.rangestatement and proof · cited by 1,341
- Nat.choosestatement and proof · cited by 494
- Finset.sum_singletonproof · cited by 251
- Nat.cast_succproof · cited by 99
- Nat.choose_zero_rightproof · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.sum_bernoulliproof · cited by 2
- Polynomial.bernoulli_eval_oneproof · cited by 2