Theorems · Theorem · logic and foundations
Ordinal.sSup_le_sSup_add_one
∀ (s : Set Ordinal.{u_3}), sSup s ≤ sSup ((fun x => x + 1) '' s)- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.imagestatement and proof · cited by 5,609
- LE.le.transproof · cited by 3,151
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Ordinalstatement and proof · cited by 1,688
- SupSet.sSupstatement and proof · cited by 954
- BddAboveproof · cited by 620
- Set.mem_image_of_memproof · cited by 371
- lt_add_oneproof · cited by 105
- le_csSupproof · cited by 66
- csSup_of_not_bddAboveproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.iSup_le_iSup_add_oneproof · cited by 2
- Ordinal.sSup_lt_of_lt_cofproof · cited by 1