Theorems · Theorem · logic and foundations
Ordinal.opow_add_one
∀ (a b : Ordinal.{u_1}), a ^ (b + 1) = a ^ b * a- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- iSupproof · cited by 2,415
- MulZeroClass.mul_zeroproof · cited by 2,091
- Ordinalstatement and proof · cited by 1,688
- LT.lt.ne'proof · cited by 1,417
- Set.Iioproof · cited by 1,166
- eq_or_neproof · cited by 1,117
- zero_lt_oneproof · cited by 598
- Order.IsSuccLimitproof · cited by 255
- Ordinal.limitRecOnproof · cited by 20
- Ordinal.zero_opowproof · cited by 13
- add_pos_of_rightproof · cited by 8
Cited by9
Results whose statement or proof uses this declaration.
- Ordinal.opow_posproof · cited by 22
- Ordinal.opow_oneproof · cited by 14
- Ordinal.opow_succproof · cited by 11
- Ordinal.one_opowproof · cited by 9
- Ordinal.opow_addproof · cited by 9
- Ordinal.opow_mulproof · cited by 4
- Ordinal.opow_le_opow_leftproof · cited by 4
- Ordinal.card_opow_le_of_omega0_le_leftproof · cited by 3
- ONote.repr_opow_aux₂proof · cited by 1