Theorems · Theorem · number theory
Nat.le_log_of_pow_le
∀ {b x y : ℕ}, 1 < b → b ^ x ≤ y → x ≤ Nat.log b y- Defined in
- Mathlib.Data.Nat.Log
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.transproof · cited by 370
- LE.le.not_gtproof · cited by 189
- Nat.logstatement · cited by 101
- ne_or_eqproof · cited by 32
- Nat.le_log_iff_pow_leproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Nat.lt_pow_of_log_ltproof · cited by 3
- Nat.factorization_lcmUptoproof · cited by 3
- padicValNat_le_nat_logproof · cited by 2
- Nat.log_monotoneproof · cited by 2
- Chebyshev.psi_eq_sum_mul_log_primeproof · cited by 2
- Nat.log_anti_leftproof · cited by 2
- Nat.emultiplicity_eq_card_pow_dvdproof · cited by 1
- Nat.max_log_padicValNat_succ_eq_log_succproof · cited by 1