Theorems · Theorem · logic and foundations
Ordinal.addCommute_iff_eq_mul_natCast
∀ {o₁ o₂ : Ordinal.{u_1}}, AddCommute o₁ o₂ ↔ ∃ o n₁ n₂, o * ↑n₁ = o₁ ∧ o * ↑n₂ = o₂- Defined in
- Mathlib.SetTheory.Ordinal.Commute
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- Ordinalstatement and proof · cited by 1,688
- add_commproof · cited by 1,535
- eq_or_neproof · cited by 1,117
- Nat.cast_addproof · cited by 586
- mul_addproof · cited by 413
- AddCommutestatement and proof · cited by 185
- add_left_cancelproof · cited by 29
- WellFoundedLT.inductionproof · cited by 24
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