Theorems · Theorem · logic and foundations
Ordinal.op_eq_self_of_isPrincipal
∀ {a o : Ordinal.{u}} {op : Ordinal.{u} → Ordinal.{u} → Ordinal.{u}},
a < o → Order.IsNormal (op a) → Ordinal.IsPrincipal op o → Order.IsSuccLimit o → op a o = o- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- LT.lt.leproof · cited by 2,189
- Ordinalstatement and proof · cited by 1,688
- Set.Iioproof · cited by 1,166
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.IsNormalstatement and proof · cited by 118
- LE.le.antisymm'proof · cited by 104
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Order.IsNormal.strictMonoproof · cited by 44
- StrictMono.le_applyproof · cited by 32
- Ordinal.iSup_le_iffproof · cited by 9
- Order.IsNormal.apply_of_isSuccLimitproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_iff_add_left_eq_selfproof · cited by 3
- Ordinal.isPrincipal_mul_iff_mul_left_eqproof · cited by 3
- Ordinal.op_eq_self_of_principalproof · cited by 0