Theorems · Theorem · logic and foundations
Ordinal.isSuccLimit_of_isPrincipal_add
∀ {o : Ordinal.{u}}, 1 < o → Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) o → Order.IsSuccLimit o- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Order.IsSuccLimitstatement · cited by 255
- Ordinal.IsPrincipalstatement and proof · cited by 92
- LT.lt.ne_botproof · cited by 26
- Ordinal.isSuccLimit_iffproof · cited by 6
- Order.isSuccPrelimit_iff_succ_ltproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_iff_add_left_eq_selfproof · cited by 3
- Ordinal.isSuccLimit_of_isPrincipal_mulproof · cited by 3
- Ordinal.isPrincipal_add_mul_of_isPrincipal_addproof · cited by 1
- Ordinal.isSuccLimit_of_principal_addproof · cited by 0