Theorems · Theorem · logic and foundations
Ordinal.iterate_lt_nfp
∀ {f : Ordinal.{u} → Ordinal.{u}}, StrictMono f → ∀ {a : Ordinal.{u}}, a < f a → ∀ (n : ℕ), f^[n] a < Ordinal.nfp f a- Defined in
- Mathlib.SetTheory.Ordinal.FixedPoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement and proof · cited by 1,688
- Nat.iteratestatement · cited by 740
- StrictMonostatement and proof · cited by 706
- LT.lt.trans_leproof · cited by 678
- Ordinal.nfpstatement and proof · cited by 41
- Function.iterate_succ_applyproof · cited by 18
- StrictMono.iterateproof · cited by 3
- Ordinal.iterate_le_nfpproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.iterate_omega0_opow_lt_epsilon_zeroproof · cited by 2
- Ordinal.iterate_veblen_lt_gamma_zeroproof · cited by 2