Theorems · Theorem · logic and foundations
Ordinal.omega0_ne_zero
Ordinal.omega0 ≠ 0
- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 94 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 · cited by 1,688
- LT.lt.ne'proof · cited by 1,417
- Ordinal.omega0statement · cited by 197
- Ordinal.omega0_posproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- Ordinal.isSuccLimit_omega0proof · cited by 9
- Ordinal.lt_omega0_opowproof · cited by 3
- Ordinal.natCast_add_omega0proof · cited by 3
- Ordinal.isSuccPrelimit_iff_omega0_dvdproof · cited by 2
- Ordinal.mul_eq_right_iff_opow_omega0_dvdproof · cited by 2
- Ordinal.mul_omega0_opow_opowproof · cited by 1
- Ordinal.sub_omega0_opow_log_ltproof · cited by 1
- Ordinal.eq_zero_or_opow_omega0_le_of_mul_eq_rightproof · cited by 1
- Ordinal.lt_omega0_omega0_opowproof · cited by 0
- Ordinal.nfp_mul_eq_opow_omega0proof · cited by 0