Theorems · Theorem · logic and foundations
Cardinal.noMaxOrder
∀ {c : Cardinal.{u_1}}, Cardinal.aleph0 ≤ c → NoMaxOrder c.ord.ToType- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Ordinalproof · cited by 1,688
- Cardinal.aleph0statement and proof · cited by 521
- NoMaxOrderstatement · cited by 340
- Cardinal.ordstatement and proof · cited by 266
- Order.IsSuccPrelimitproof · cited by 157
- Ordinal.ToTypestatement · cited by 143
- Order.IsSuccLimit.isSuccPrelimitproof · cited by 37
- Ordinal.type_toTypeproof · cited by 28
- Cardinal.isSuccLimit_ordproof · cited by 11
- Ordinal.isSuccPrelimit_type_lt_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directedproof · cited by 1
- Field.Emb.Cardinal.noMaxOrder_rank_toTypeproof · cited by 0
- CategoryTheory.SmallObject.prop_iterationFunctor_map_succproof · cited by 0