Theorems · Theorem · logic and foundations
Ordinal.isPrincipal_add_iff_add_left_eq_self
∀ {o : Ordinal.{u}}, Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) o ↔ ∀ 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zero_addproof · cited by 2,366
- Ordinalstatement and proof · cited by 1,688
- lt_or_geproof · cited by 182
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Order.IsNormal.strictMonoproof · cited by 44
- Ordinal.isNormal_add_rightproof · cited by 13
- Order.le_one_iffproof · cited by 10
- Ordinal.isSuccLimit_of_isPrincipal_addproof · cited by 4
- Ordinal.op_eq_self_of_isPrincipalproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.IsPrincipal.add_eq_rightproof · cited by 2
- Ordinal.isPrincipal_add_omega0proof · cited by 2
- Ordinal.principal_add_iff_add_left_eq_selfproof · cited by 0