Theorems · Theorem · logic and foundations
Ordinal.opow_natCast
∀ (a : Ordinal.{u_1}) (n : ℕ), a ^ ↑n = a ^ n- Defined in
- Mathlib.SetTheory.Ordinal.Exponential
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 45 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.
- Nat.cast_zeroproof · cited by 1,870
- Ordinalstatement and proof · cited by 1,688
- pow_zeroproof · cited by 1,094
- pow_succproof · cited by 374
- Order.succ_eq_add_oneproof · cited by 115
- Nat.cast_succproof · cited by 99
- Ordinal.opow_zeroproof · cited by 38
- Ordinal.opow_succproof · cited by 11
Cited by11
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_opow_omega0proof · cited by 3
- Ordinal.preOmega_of_omega0_sq_leproof · cited by 1
- ONote.repr_opowproof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1
- Cardinal.preBeth_of_omega0_sq_leproof · cited by 1
- Ordinal.iSup_pow_natCastproof · cited by 1
- Ordinal.card_opow_leproof · cited by 1
- Ordinal.natCast_opowproof · cited by 0
- Ordinal.one_lt_powproof · cited by 0
- Ordinal.pow_eq_one_iffproof · cited by 0
- Ordinal.natCast_logproof · cited by 0