Theorems · Theorem · number theory
Bertrand.real_main_inequality
∀ {x : ℝ}, 512 ≤ x → x * (2 * x) ^ √(2 * x) * 4 ^ (2 * x / 3) ≤ 4 ^ xA refined version of the Bertrand.main_inequality below.
This is not best possible: it actually holds for 464 ≤ x.
- Defined in
- Mathlib.NumberTheory.Bertrand
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites67
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Semiringproof · cited by 13,802
- AddCommMonoidproof · cited by 12,281
- PartialOrderproof · cited by 6,410
- Set.preimageproof · cited by 4,946
- LE.le.transproof · cited by 3,151
- Nat.cast_oneproof · cited by 2,501
- Set.extproof · cited by 2,266
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
Cited by1
Results whose statement or proof uses this declaration.
- bertrand_main_inequalityproof · cited by 1