Theorems · Theorem · number theory
Nat.pow_log_le_self
∀ (b : ℕ) {x : ℕ}, x ≠ 0 → b ^ Nat.log b x ≤ x- Defined in
- Mathlib.Data.Nat.Log
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_rflproof · cited by 1,558
- Nat.logstatement · cited by 101
- Nat.pow_le_of_le_logproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- Nat.factorization_lcmUptoproof · cited by 3
- Chebyshev.psi_le_primeCounting_mul_logproof · cited by 3
- Nat.pow_log_le_add_oneproof · cited by 2
- Int.zpow_log_le_selfproof · cited by 2
- Nat.log_mul_baseproof · cited by 2
- Nat.log_anti_leftproof · cited by 2
- Nat.log_lt_log_succ_iffproof · cited by 1
- Nat.max_log_padicValNat_succ_eq_log_succproof · cited by 1
- Nat.log_le_clogproof · cited by 0