Theorems · Theorem · logic and foundations
Ordinal.lift_cof_iSup
∀ {β : Type v} [inst : LinearOrder β] [Small.{u, v} β] [NoMaxOrder β] {f : β → Ordinal.{u}},
StrictMono f → Cardinal.lift.{v, u} (⨆ i, f i).cof = Cardinal.lift.{u, v} (Order.cof β)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderSmallNoMaxOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Cardinalstatement and proof · cited by 2,598
- iSupstatement · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- StrictMonostatement and proof · cited by 706
- Cardinal.liftstatement and proof · cited by 583
- Smallstatement and proof · cited by 369
- NoMaxOrderstatement and proof · cited by 340
- Ordinal.cofstatement and proof · cited by 125
- Order.cofstatement and proof · cited by 86
- Ordinal.lift_cof_iSup_add_oneproof · cited by 4
- Ordinal.iSup_add_oneproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.cof_iSupproof · cited by 0