Theorems · Theorem · logic and foundations
Ordinal.lt_iSup_add_one
∀ {ι : Type u_3} (f : ι → Ordinal.{u}) [Small.{u, u_3} ι] (i : ι), f i < ⨆ i, f i + 1- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 3 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- Smallstatement and proof · cited by 369
- Ordinal.le_iSupproof · cited by 19
- Order.add_one_le_iffproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.lt_lsubproof · cited by 7
- Ordinal.cof_lift_iSup_add_one_leproof · cited by 2
- MeasurableSpace.generateMeasurableRec_omega_oneproof · cited by 1