Theorems · Theorem · logic and foundations
Ordinal.IsPrincipal.mul_natCast_lt
∀ {a o : Ordinal.{u}}, Ordinal.IsPrincipal (fun x1 x2 => x1 + x2) o → a < o → ∀ (n : ℕ), a * ↑n < o- Defined in
- Mathlib.SetTheory.Ordinal.Principal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Ordinalstatement and proof · cited by 1,688
- Ordinal.IsPrincipalstatement and proof · cited by 92
- Nat.cast_add_oneproof · cited by 56
- LT.lt.posproof · cited by 30
- mul_add_oneproof · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.isPrincipal_add_iff_zero_or_omega0_opowproof · cited by 3