Theorems · Theorem · logic and foundations
Ordinal.nfp_le_fp
∀ {f : Ordinal.{u} → Ordinal.{u}}, Monotone f → ∀ {a b : Ordinal.{u}}, a ≤ b → f b ≤ b → Ordinal.nfp f a ≤ b- Defined in
- Mathlib.SetTheory.Ordinal.FixedPoint
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Monotonestatement and proof · cited by 1,397
- Ordinal.nfpstatement · cited by 41
- Ordinal.nfpFamily_le_fpproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Ordinal.epsilon_zero_le_of_omega0_opow_leproof · cited by 1
- Ordinal.gamma_zero_le_of_veblen_leproof · cited by 1
- Ordinal.eq_zero_or_opow_omega0_le_of_mul_eq_rightproof · cited by 1
- Ordinal.nfp_mul_opow_omega0_addproof · cited by 1
- Ordinal.nfp_mul_eq_opow_omega0proof · cited by 0
- Ordinal.nfp_add_eq_mul_omega0proof · cited by 0