Theorems · Theorem · logic and foundations
Ordinal.natCast_add_omega0
∀ (n : ℕ), ↑n + Ordinal.omega0 = Ordinal.omega0
- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 95 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.
- le_antisymmproof · cited by 2,068
- Ordinalstatement and proof · cited by 1,688
- LE.le.trans_ltproof · cited by 795
- Ordinal.omega0statement and proof · cited by 197
- le_add_selfproof · cited by 51
- le_of_forall_ltproof · cited by 25
- Ordinal.natCast_lt_omega0proof · cited by 24
- Ordinal.lt_omega0proof · cited by 15
- Ordinal.omega0_ne_zeroproof · cited by 10
- Ordinal.lt_add_iffproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.one_add_omega0proof · cited by 5
- Ordinal.natCast_add_of_omega0_leproof · cited by 1
- Ordinal.add_omega0proof · cited by 1