Theorems · Theorem · logic and foundations
Ordinal.lt_opow_succ_log_self
∀ {b : Ordinal.{u_1}}, 1 < b → ∀ (x : Ordinal.{u_1}), x < b ^ Order.succ (Ordinal.log b x)- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- Ordinalstatement and proof · cited by 1,688
- eq_or_neproof · cited by 1,117
- Order.succstatement and proof · cited by 633
- Order.succ_eq_add_oneproof · cited by 115
- Ordinal.logstatement and proof · cited by 45
- LT.lt.posproof · cited by 30
- Order.lt_succ_iffproof · cited by 22
- Ordinal.opow_oneproof · cited by 14
- Ordinal.log_zero_rightproof · cited by 8
- Ordinal.lt_opow_iff_log_ltproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Ordinal.div_opow_log_ltproof · cited by 4
- Ordinal.isPrincipal_add_iff_zero_or_omega0_opowproof · cited by 3
- Ordinal.log_opow_mul_addproof · cited by 2
- Ordinal.log_eq_iffproof · cited by 2
- Ordinal.mul_eq_opow_log_succproof · cited by 0