Theorems · Theorem · combinatorics
Nat.succ_dvd_centralBinom
∀ (n : ℕ), n + 1 ∣ n.centralBinom
A crucial lemma to ensure that Catalan numbers can be defined via their explicit formula
catalan n = n.centralBinom / (n + 1).
- Defined in
- Mathlib.Data.Nat.Choose.Central
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- add_assocproof · cited by 746
- two_mulproof · cited by 232
- zero_lt_twoproof · cited by 124
- mul_dvd_mul_leftproof · cited by 34
- Nat.centralBinomstatement and proof · cited by 24
- Nat.coprime_add_self_rightproof · cited by 3
- Nat.succ_mul_centralBinom_succproof · cited by 2
- Nat.two_dvd_centralBinom_succproof · cited by 2
- Nat.coprime_self_add_leftproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- catalan_eq_centralBinom_divproof · cited by 3
- succ_mul_catalan_eq_centralBinomproof · cited by 0