Theorems · Theorem · logic and foundations
Ordinal.mem_range_deriv
∀ {f : Ordinal.{u} → Ordinal.{u}}, Order.IsNormal f → ∀ {a : Ordinal.{u}}, a ∈ Set.range (Ordinal.deriv f) ↔ f a = a- Defined in
- Mathlib.SetTheory.Ordinal.FixedPoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Set.rangestatement · cited by 4,705
- Ordinalstatement and proof · cited by 1,688
- Order.IsNormalstatement and proof · cited by 118
- Set.mem_rangeproof · cited by 102
- LE.le.ge_iff_eq'proof · cited by 50
- Order.IsNormal.strictMonoproof · cited by 44
- StrictMono.le_applyproof · cited by 32
- Ordinal.derivstatement and proof · cited by 26
- Ordinal.le_iff_derivproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.add_eq_right_iff_mul_omega0_leproof · cited by 2
- Ordinal.mem_range_gammaproof · cited by 1