Theorems · Definition · logic and foundations
Order.cof
(α : Type u) → [Preorder α] → Cardinal.{u}The cofinality of a preorder is the smallest cardinality of a cofinal subset.
- Cited by
- 86 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by89
Results whose statement or proof uses this declaration.
- Ordinal.cofproof · cited by 125
- Order.cof_lestatement · cited by 13
- Ordinal.cof_typestatement and proof · cited by 9
- Ordinal.lift_cofproof · cited by 8
- Ordinal.cof_toTypestatement and proof · cited by 7
- Order.cof_eq_cardinalMkstatement and proof · cited by 6
- Order.exists_cof_eqstatement · cited by 6
- Ordinal.exists_ord_cof_eqstatement and proof · cited by 5
- Order.cof_le_cardinalMkstatement · cited by 5
- Order.cof_eq_one_iffstatement and proof · cited by 4
- Order.cof_lt_aleph0_iffstatement and proof · cited by 4
- OrderIso.lift_cof_congrstatement · cited by 4