Theorems · Theorem · logic and foundations
Cardinal.exists_ord_eq
∀ (α : Type u_1), ∃ r, ∃ (x : IsWellOrder α r), (Cardinal.mk α).ord = Ordinal.type r
There exists a well-order on α whose order type is exactly ord #α.
- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangeproof · cited by 4,705
- iInfproof · cited by 1,690
- Ordinalstatement · cited by 1,688
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.ordstatement and proof · cited by 266
- Ordinal.typestatement and proof · cited by 207
- IsWellOrderstatement and proof · cited by 171
- ciInf_memproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Cardinal.card_ordproof · cited by 23
- Cardinal.gc_ord_cardproof · cited by 6
- Ordinal.exists_ord_cof_eqproof · cited by 5
- Cardinal.exists_ord_eq_type_ltproof · cited by 3
- Cardinal.ord_eqproof · cited by 1
- Cardinal.mk_subset_mk_lt_cofproof · cited by 0
- Ordinal.le_cof_iff_blsubproof · cited by 0
- Ordinal.exists_blsub_cofproof · cited by 0