Theorems · Theorem · logic and foundations
Ordinal.opow_zero
∀ (a : Ordinal.{u_1}), a ^ 0 = 1- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 42 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.
- Set.Elemproof · cited by 7,166
- iSupproof · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- Set.Iioproof · cited by 1,166
- eq_or_neproof · cited by 1,117
- Order.IsSuccLimitproof · cited by 255
- Ordinal.sub_zeroproof · cited by 3
- Ordinal.zero_opow'proof · cited by 3
- Ordinal.limitRecOn_zeroproof · cited by 2
Cited by38
Results whose statement or proof uses this declaration.
- Ordinal.opow_posproof · cited by 22
- Ordinal.opow_oneproof · cited by 14
- Ordinal.opow_log_le_selfproof · cited by 11
- Ordinal.opow_natCastproof · cited by 11
- Ordinal.one_opowproof · cited by 9
- Ordinal.opow_addproof · cited by 9
- Ordinal.opow_le_iff_le_logproof · cited by 8
- Ordinal.isPrincipal_add_omega0_opowproof · cited by 7
- ONote.fundamentalSequence_has_propproof · cited by 5
- Ordinal.opow_le_opow_leftproof · cited by 4
- Ordinal.opow_mulproof · cited by 4
- Ordinal.veblen_zero_strictMonoproof · cited by 4