Theorems · Theorem · combinatorics
Nat.four_pow_lt_mul_centralBinom
∀ (n : ℕ), 4 ≤ n → 4 ^ n < n * n.centralBinom
An exponential lower bound on the central binomial coefficient. This bound is of interest because it appears in [Tochiori's refinement of Erdős's proof of Bertrand's postulate](tochiori_bertrand).
- Defined in
- Mathlib.Data.Nat.Choose.Central
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 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.
- add_zeroproof · cited by 2,707
- Nat.cast_oneproof · cited by 2,501
- mul_assocproof · cited by 1,667
- Nat.cast_addproof · cited by 586
- le_of_not_gtproof · cited by 430
- Nat.cast_mulproof · cited by 309
- not_ltproof · cited by 306
- neg_neg_of_posproof · cited by 227
- lt_trichotomyproof · cited by 178
- mul_lt_mul_of_pos_leftproof · cited by 71
- Nat.strong_induction_onproof · cited by 52
- Nat.centralBinomstatement and proof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- Nat.exists_prime_lt_and_le_two_mul_eventuallyproof · cited by 1
- Nat.four_pow_le_two_mul_self_mul_centralBinomproof · cited by 0