Theorems · Theorem · logic and foundations
Ordinal.natCast_lt_omega0
∀ (n : ℕ), ↑n < Ordinal.omega0
- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ordinalstatement · cited by 1,688
- Ordinal.omega0statement · cited by 197
- Ordinal.lt_omega0proof · cited by 15
Cited by24
Results whose statement or proof uses this declaration.
- Ordinal.one_lt_omega0proof · cited by 39
- Ordinal.omega0_posproof · cited by 14
- Ordinal.isSuccLimit_omega0proof · cited by 9
- ONote.NFBelow.repr_ltproof · cited by 7
- Ordinal.isPrincipal_add_omega0_opowproof · cited by 7
- ONote.fundamentalSequence_has_propproof · cited by 5
- Ordinal.isPrincipal_mul_omega0proof · cited by 4
- Ordinal.iSup_natCastproof · cited by 4
- Ordinal.lt_omega0_opowproof · cited by 3
- Ordinal.natCast_add_omega0proof · cited by 3
- Ordinal.omega0_leproof · cited by 2
- Ordinal.card_opow_le_of_omega0_le_rightproof · cited by 2