Theorems · Theorem · combinatorics
Nat.add_one_mul_choose_eq
∀ (n k : ℕ), (n + 1) * n.choose k = (n + 1).choose (k + 1) * (k + 1)
- Defined in
- Mathlib.Data.Nat.Choose.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
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 by7
Results whose statement or proof uses this declaration.
- Nat.choose_succ_right_eqproof · cited by 5
- Polynomial.bernoulli_comp_one_add_Xproof · cited by 2
- bernsteinPolynomial.derivative_succ_auxproof · cited by 1
- Nat.factorization_le_factorization_choose_addproof · cited by 1
- Nat.Prime.emultiplicity_le_emultiplicity_choose_addproof · cited by 1
- Polynomial.eval_monomial_one_add_subproof · cited by 0
- Nat.succ_mul_binomialproof · cited by 0