Theorems · Theorem · logic and foundations
Ordinal.IsPrincipal.sSup
∀ {op : Ordinal.{u_1} → Ordinal.{u_1} → Ordinal.{u_1}} {s : Set Ordinal.{u_1}},
(∀ x ∈ s, Ordinal.IsPrincipal op x) → Ordinal.IsPrincipal op (sSup s)- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- 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.Nonemptyproof · cited by 2,627
- Ordinalstatement and proof · cited by 1,688
- SupSet.sSupstatement and proof · cited by 954
- BddAboveproof · cited by 620
- Set.eq_empty_or_nonemptyproof · cited by 248
- bot_eq_zero'proof · cited by 92
- Ordinal.IsPrincipalstatement and proof · cited by 92
- lt_max_of_lt_rightproof · cited by 29
- csSup_emptyproof · cited by 28
- csSup_of_not_bddAboveproof · cited by 16
- lt_max_of_lt_leftproof · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.IsPrincipal.iSupproof · cited by 1
- Ordinal.Principal.sSupproof · cited by 0