Theorems · Theorem · logic and foundations
Ordinal.type_ne_zero_iff_nonempty
∀ {α : Type u} {r : α → α → Prop} [inst : IsWellOrder α r], Ordinal.type r ≠ 0 ↔ Nonempty α- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 33 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement · cited by 1,688
- Ordinal.typestatement · cited by 207
- IsWellOrderstatement and proof · cited by 171
Cited by4
Results whose statement or proof uses this declaration.
- Ordinal.nonempty_toType_iffproof · cited by 3
- Ordinal.IsNormal.bsupproof · cited by 1
- Ordinal.isClosed_iff_bsupproof · cited by 0
- Ordinal.type_ne_zero_of_nonemptyproof · cited by 0