Theorems · Theorem · logic and foundations
Ordinal.isPrincipal_add_iff_add_lt_ne_self
∀ {a : Ordinal.{u}}, Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) a ↔ ∀ b < a, ∀ c < a, b + c ≠ a- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- LT.lt.neproof · cited by 872
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Ordinal.exists_lt_add_of_not_isPrincipal_addproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.principal_add_iff_add_lt_ne_selfproof · cited by 0