Theorems · Theorem · logic and foundations
Ordinal.div_opow_log_lt
∀ {b : Ordinal.{u_1}} (o : Ordinal.{u_1}), 1 < b → o / b ^ Ordinal.log b o < b- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement and proof · cited by 1,688
- LT.lt.ne'proof · cited by 1,417
- zero_lt_oneproof · cited by 598
- LT.lt.transproof · cited by 370
- Ordinal.logstatement and proof · cited by 45
- Ordinal.opow_posproof · cited by 22
- Ordinal.opow_succproof · cited by 11
- Ordinal.lt_mul_iff_div_ltproof · cited by 8
- Ordinal.lt_opow_succ_log_selfproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Ordinal.lt_omega0_opowproof · cited by 3
- Ordinal.div_two_opow_logproof · cited by 1
- Ordinal.sub_omega0_opow_log_ltproof · cited by 1
- Ordinal.CNF.snd_ltproof · cited by 0