Theorems · Theorem · number theory
Int.zpow_log_le_self
∀ {R : Type u_1} [inst : Semifield R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] [inst_3 : FloorSemiring R]
{b : ℕ} {r : R}, 1 < b → 0 < r → ↑b ^ Int.log b r ≤ r- Defined in
- Mathlib.Data.Int.Log
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- IsStrictOrderedRingstatement and proof · cited by 2,490
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- Semifieldstatement and proof · cited by 439
- le_totalproof · cited by 294
- zpow_natCastproof · cited by 271
- Nat.floorproof · cited by 215
- zpow_negproof · cited by 198
- FloorSemiringstatement and proof · cited by 179
- Nat.ceilproof · cited by 141
- Nat.cast_powproof · cited by 131
Cited by2
Results whose statement or proof uses this declaration.
- Real.floor_logb_natCastproof · cited by 2
- Int.self_le_zpow_clogproof · cited by 1