Theorems · Theorem · logic and foundations
Ordinal.mul_omega0
∀ {a : Ordinal.{u}}, 0 < a → a < Ordinal.omega0 → a * Ordinal.omega0 = Ordinal.omega0- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 3 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 and proof · cited by 1,688
- Ordinal.omega0statement and proof · cited by 197
- Ordinal.isPrincipal_mul_omega0proof · cited by 4
- Ordinal.isPrincipal_mul_iff_mul_left_eqproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.mul_omega0_dvdproof · cited by 1
- Ordinal.mul_omega0_opow_opowproof · cited by 1
- Ordinal.natCast_mul_omega0proof · cited by 0