Theorems · Theorem · group theory
QuaternionGroup.orderOf_xa
∀ {n : ℕ} [NeZero n] (i : ZMod (2 * n)), orderOf (QuaternionGroup.xa i) = 4If 0 < n, then xa i has order 4.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factproof · cited by 2,726
- Nat.Primeproof · cited by 2,059
- ZModstatement and proof · cited by 1,024
- pow_oneproof · cited by 894
- orderOfstatement · cited by 324
- ZMod.valproof · cited by 159
- NeZero.posproof · cited by 57
- Nat.prime_twoproof · cited by 55
- QuaternionGroupstatement · cited by 22
- ZMod.val_natCastproof · cited by 18
- ZMod.val_zeroproof · cited by 12
- orderOf_eq_prime_powproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- QuaternionGroup.quaternionGroup_one_isCyclicproof · cited by 0
- QuaternionGroup.exponentproof · cited by 0