Theorems · Theorem · logic and foundations
Ordinal.ord_mk_lt_type
∀ {α : Type u} (r : α → α → Prop) [inst : IsWellOrder α r] {s : Set α},
s.Finite → sᶜ.Nonempty → (Cardinal.mk ↑s).ord < Ordinal.type r- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Compl.complstatement and proof · cited by 2,925
- Set.Nonemptystatement and proof · cited by 2,627
- Cardinalproof · cited by 2,598
- le_reflproof · cited by 2,061
- Set.Finitestatement and proof · cited by 1,814
- Ordinalstatement · cited by 1,688
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.ordstatement and proof · cited by 266
- Ordinal.typestatement · cited by 207
- IsWellOrderstatement and proof · cited by 171
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.not_lt_enum_ord_mk_min_complstatement and proof · cited by 0