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Theorems · Theorem · number theory

Nat.log_lt_self

∀ (b : ℕ) {x : ℕ}, x ≠ 0 → Nat.log b x < x
Defined in
Mathlib.Data.Nat.Log
Cited by
2 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Nat.log_le_self · cited by 0Nat.log_le_selfpadicValNat_add_le_self · cited by 0padicValNat_add_le_selfle_or_gt · cited by 269le_or_gtNat.log · cited by 101Nat.logNat.log_of_left_le_one · cited by 12Nat.log_of_left_le_oneNat.log_lt_of_lt_pow · cited by 4Nat.log_lt_of_lt_powNat.log_lt_selfCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.