Theorems · Theorem · logic and foundations
Ordinal.natCast_lt_of_isSuccLimit
∀ {o : Ordinal.{u_4}}, Order.IsSuccLimit o → ∀ (n : ℕ), ↑n < o- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zero_addproof · cited by 2,366
- Ordinalstatement and proof · cited by 1,688
- Order.IsSuccLimitstatement and proof · cited by 255
- bot_eq_zero'proof · cited by 92
- Order.IsSuccLimit.bot_ltproof · cited by 13
- Order.IsSuccLimit.add_natCast_ltproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.isSuccPrelimit_iff_omega0_dvdproof · cited by 2
- Ordinal.omega0_le_of_isSuccLimitproof · cited by 2
- Ordinal.one_lt_of_isSuccLimitproof · cited by 1