Theorems · Theorem · logic and foundations
Ordinal.IsInitial.isPrincipal_add
∀ {o : Ordinal.{u_1}}, o.IsInitial → Ordinal.omega0 ≤ o → Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) o- Defined in
- Mathlib.SetTheory.Cardinal.Ordinal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement and proof · cited by 1,688
- Ordinal.omega0statement and proof · cited by 197
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Ordinal.IsInitialstatement and proof · cited by 28
- Ordinal.aleph0_le_cardproof · cited by 5
- Ordinal.IsInitial.ord_cardproof · cited by 4
- Ordinal.isPrincipal_add_ordproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_omegaproof · cited by 1
- Ordinal.IsInitial.principal_addproof · cited by 0