Theorems · Theorem · logic and foundations
Ordinal.omega0_pos
0 < Ordinal.omega0
- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 93 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.natCast_lt_omega0proof · cited by 24
Cited by14
Results whose statement or proof uses this declaration.
- Ordinal.omega0_ne_zeroproof · cited by 10
- ONote.NFBelow.repr_ltproof · cited by 7
- ONote.fundamentalSequence_has_propproof · cited by 5
- ONote.omega0_le_oaddproof · cited by 5
- Ordinal.card_opow_le_of_omega0_le_leftproof · cited by 3
- ONote.repr_opow_aux₁proof · cited by 1
- ONote.repr_opow_aux₂proof · cited by 1
- Ordinal.lt_omega0_opow_succproof · cited by 1
- Ordinal.mul_lt_omega0_opowproof · cited by 1
- ONote.oadd_posproof · cited by 1
- ONote.split_add_ltproof · cited by 1
- Ordinal.card_opow_eq_of_omega0_le_rightproof · cited by 1