Theorems · Theorem · logic and foundations
Ordinal.isPrincipal_mul_iff_mul_left_eq
∀ {o : Ordinal.{u}}, Ordinal.IsPrincipal (fun x1 x2 => x1 * x2) o ↔ ∀ (a : Ordinal.{u}), 0 < a → a < o → a * o = o- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- le_antisymmproof · cited by 2,068
- Ordinalstatement and proof · cited by 1,688
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- LT.lt.trans_leproof · cited by 678
- le_or_gtproof · cited by 269
- pos_iff_ne_zeroproof · cited by 180
- Ordinal.IsPrincipalstatement and proof · cited by 92
- one_add_one_eq_twoproof · cited by 65
- Order.IsNormal.strictMonoproof · cited by 44
- Order.one_le_iff_posproof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.mul_omega0proof · cited by 3
- Ordinal.isPrincipal_mul_omega0_opow_opowproof · cited by 2
- Ordinal.principal_mul_iff_mul_left_eqproof · cited by 0