Theorems · Theorem · logic and foundations
Ordinal.card_opow_eq_of_omega0_le_left
∀ {a b : Ordinal.{u_1}}, Ordinal.omega0 ≤ a → 0 < b → (a ^ b).card = max a.card b.card- Defined in
- Mathlib.SetTheory.Cardinal.Ordinal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- LT.lt.trans_leproof · cited by 678
- LE.le.antisymmproof · cited by 507
- Ordinal.omega0statement and proof · cited by 197
- Ordinal.cardstatement · cited by 122
- max_leproof · cited by 71
- Ordinal.one_lt_omega0proof · cited by 39
- Ordinal.card_le_cardproof · cited by 10
- Ordinal.right_le_opowproof · cited by 4
- Ordinal.card_opow_le_of_omega0_le_leftproof · cited by 3
- Ordinal.left_le_opowproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.card_omega0_opowproof · cited by 0