Theorems · Theorem · number theory
Chebyshev.psi_le
∀ {x : ℝ}, 1 ≤ x → Chebyshev.psi x ≤ Real.log 4 * x + 2 * √x * Real.log xExplicit upper bound on ψ.
- Defined in
- Mathlib.NumberTheory.Chebyshev
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- le_transproof · cited by 985
- Real.logstatement and proof · cited by 939
- add_le_addproof · cited by 666
- Real.sqrtstatement and proof · cited by 545
- le_of_not_gtproof · cited by 430
- neg_neg_of_posproof · cited by 227
- le_abs_selfproof · cited by 113
- Chebyshev.thetaproof · cited by 38
- Chebyshev.psistatement and proof · cited by 34
Cited by1
Results whose statement or proof uses this declaration.
- Chebyshev.psi_le_const_mul_selfproof · cited by 1