Theorems · Theorem · logic and foundations
Ordinal.log_eq_iff
∀ {b x : Ordinal.{u_1}}, 1 < b → x ≠ 0 → ∀ (y : Ordinal.{u_1}), Ordinal.log b x = y ↔ b ^ y ≤ x ∧ x < b ^ (y + 1)- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 2 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_antisymmproof · cited by 2,068
- Ordinalstatement and proof · cited by 1,688
- Ordinal.logstatement and proof · cited by 45
- Order.lt_add_one_iffproof · cited by 13
- Ordinal.opow_log_le_selfproof · cited by 11
- Ordinal.opow_le_iff_le_logproof · cited by 8
- Ordinal.lt_opow_succ_log_selfproof · cited by 5
- Ordinal.lt_opow_iff_log_ltproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.log_opow_mul_addproof · cited by 2
- Ordinal.natCast_logproof · cited by 0