Theorems · Theorem · logic and foundations
Ordinal.bounded_singleton
∀ {α : Type u_1} {r : α → α → Prop} [inst : IsWellOrder α r],
Order.IsSuccLimit (Ordinal.type r) → ∀ (x : α), Set.Bounded r {x}- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsWellOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Ordinalstatement · cited by 1,688
- Order.succproof · cited by 633
- Order.IsSuccLimitstatement and proof · cited by 255
- Ordinal.typestatement and proof · cited by 207
- Set.mem_singleton_iffproof · cited by 172
- IsWellOrderstatement and proof · cited by 171
- PrincipalSeg.toRelEmbeddingproof · cited by 129
- Ordinal.typeinproof · cited by 60
- Set.Boundedstatement · cited by 57
- Order.lt_succproof · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.mk_bounded_subsetproof · cited by 1