Theorems · Theorem · logic and foundations
Ordinal.cof_lsub_def_nonempty
Deprecated since 2026-03-27Mathlib marks this declaration as deprecated.
∀ (o : Ordinal.{u}), {a | ∃ ι f, Ordinal.lsub f = o ∧ Cardinal.mk ι = a}.NonemptyThe set in the lsub characterization of cof is nonempty.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Set.ofPredstatement · cited by 6,101
- Set.Nonemptystatement · cited by 2,627
- Cardinalstatement · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- Cardinal.mkstatement · cited by 942
- Ordinal.ToTypeproof · cited by 143
- PrincipalSeg.toRelEmbeddingproof · cited by 129
- Ordinal.cardproof · cited by 122
- Ordinal.typeinproof · cited by 60
- Ordinal.lsubstatement · cited by 43
- Cardinal.mk_toTypeproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.cof_eq_sInf_lsubproof · cited by 2
- Ordinal.exists_lsub_cofproof · cited by 2
- Ordinal.le_cof_iff_lsubproof · cited by 1