Theorems · Theorem · logic and foundations
Ordinal.succ_lt_iSup_of_ne_iSup
∀ {ι : Type u_3} {f : ι → Ordinal.{u}} [Small.{u, u_3} ι],
(∀ (i : ι), f i ≠ iSup f) → ∀ {a : Ordinal.{u}}, a < iSup f → Order.succ a < iSup f- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement and proof · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- LT.lt.trans_leproof · cited by 678
- Order.succstatement and proof · cited by 633
- Smallstatement and proof · cited by 369
- LT.lt.not_geproof · cited by 305
- LE.le.lt_of_neproof · cited by 116
- Ordinal.le_iSupproof · cited by 19
- Ordinal.iSup_leproof · cited by 18
- Order.le_of_lt_succproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.iSup_eq_lsub_iffproof · cited by 1
- Ordinal.bsup_not_succ_of_ne_bsupproof · cited by 0