Theorems · Theorem · logic and foundations
Ordinal.isSuccLimit_opow_left
∀ {a b : Ordinal.{u_1}}, Order.IsSuccLimit a → b ≠ 0 → Order.IsSuccLimit (a ^ b)- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- Ordinalstatement and proof · cited by 1,688
- Order.succproof · cited by 633
- Order.IsSuccLimitstatement and proof · cited by 255
- Ordinal.opow_posproof · cited by 22
- Order.IsSuccLimit.bot_ltproof · cited by 13
- Ordinal.opow_succproof · cited by 11
- Ordinal.isSuccLimit_mul_rightproof · cited by 5
- Ordinal.zero_or_succ_or_isSuccLimitproof · cited by 5
- Ordinal.isSuccLimit_opowproof · cited by 2
- Ordinal.one_lt_of_isSuccLimitproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.mul_omega0_opow_opowproof · cited by 1