Theorems · Theorem · logic and foundations
Ordinal.iterate_omega0_opow_lt_epsilon_zero
∀ (n : ℕ), (fun a => Ordinal.omega0 ^ a)^[n] 0 < Ordinal.epsilon 0
ω ^ ω ^ … ^ 0 < ε₀
- Defined in
- Mathlib.SetTheory.Ordinal.Veblen
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 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.
- Ordinalstatement and proof · cited by 1,688
- Nat.iteratestatement and proof · cited by 740
- Ordinal.omega0statement and proof · cited by 197
- Order.IsNormal.strictMonoproof · cited by 44
- Ordinal.one_lt_omega0proof · cited by 39
- Ordinal.opow_zeroproof · cited by 38
- Ordinal.isNormal_opowproof · cited by 37
- Ordinal.epsilonstatement · cited by 18
- Ordinal.epsilon_zero_eq_nfpproof · cited by 4
- Ordinal.iterate_lt_nfpproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Ordinal.omega0_lt_epsilonproof · cited by 2
- Ordinal.iterate_omega0_opow_lt_epsilon0proof · cited by 0