Theorems · Theorem · logic and foundations
Ordinal.iSup_add_one
∀ {β : Type u_3} [inst : LinearOrder β] [NoMaxOrder β] {f : β → Ordinal.{u}}, StrictMono f → ⨆ i, f i + 1 = ⨆ i, f i- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderNoMaxOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- le_reflproof · cited by 2,061
- Ordinalstatement and proof · cited by 1,688
- SupSet.sSupproof · cited by 954
- StrictMonostatement and proof · cited by 706
- BddAboveproof · cited by 620
- NoMaxOrderstatement and proof · cited by 340
- LE.le.trans'proof · cited by 140
- LE.le.antisymm'proof · cited by 104
- NoMaxOrder.exists_gtproof · cited by 62
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.iSup_Iio_add_oneproof · cited by 2
- Ordinal.lift_cof_iSupproof · cited by 1