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Theorems · Theorem · logic and foundations

Ordinal.type_eq_one_of_unique

∀ {α : Type u} (r : α → α → Prop) [inst : IsWellOrder α r] [Nonempty α] [Subsingleton α], Ordinal.type r = 1
Defined in
Mathlib.SetTheory.Ordinal.Basic
Cited by
2 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
IsWellOrderNonemptySubsingleton
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Ordinal.lift_one · cited by 13Ordinal.lift_oneOrdinal.type_eq_one_iff_unique · cited by 0Ordinal.type_eq_one_iff_u…Ordinal · cited by 1688OrdinalUnique · cited by 400UniqueOrdinal.type · cited by 207Ordinal.typeIsWellOrder · cited by 171IsWellOrdernonempty_unique · cited by 11nonempty_uniqueRelIso.ordinalType_congr · cited by 7RelIso.ordinalType_congrRelIso.ofUniqueOfIrrefl · cited by 1RelIso.ofUniqueOfIrreflOrdinal.type_eq_one_of_uniqueCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.