Theorems · Theorem · logic and foundations
Ordinal.type_fintype
∀ {α : Type u} (r : α → α → Prop) [inst : IsWellOrder α r] [inst_1 : Fintype α], Ordinal.type r = ↑(Fintype.card α)- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsWellOrderFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Cardinalproof · cited by 2,598
- Ordinalstatement · cited by 1,688
- Fintype.cardstatement and proof · cited by 1,386
- Ordinal.typestatement · cited by 207
- IsWellOrderstatement and proof · cited by 171
- Cardinal.mk_fintypeproof · cited by 81
- Ordinal.card_typeproof · cited by 7
- Ordinal.card_eq_natproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Ordinal.typein_lt_natproof · cited by 1
- Ordinal.typein_lt_finproof · cited by 1
- ONote.repr_opowproof · cited by 1
- Ordinal.type_finproof · cited by 0