Theorems · Theorem · logic and foundations
RelIso.ordinalType_congr
∀ {α β : Type u_1} {r : α → α → Prop} {s : β → β → Prop} [inst : IsWellOrder α r] [inst_1 : IsWellOrder β s]
(h : r ≃r s), Ordinal.type r = Ordinal.type s- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
- Assumes
- IsWellOrderIsWellOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement · cited by 1,688
- RelIsostatement and proof · cited by 456
- Ordinal.typestatement · cited by 207
- IsWellOrderstatement and proof · cited by 171
- Ordinal.type_eqproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Ordinal.type_eq_zero_of_emptyproof · cited by 3
- RelIso.ordinal_lift_type_eqproof · cited by 3
- Ordinal.type_eq_one_of_uniqueproof · cited by 2
- OrderIso.ordinalType_congrproof · cited by 2
- Ordinal.typein_topproof · cited by 1
- RelIso.ordinal_type_eqproof · cited by 0
- Ordinal.type_preimageproof · cited by 0