Theorems · Theorem · group theory
addOrderOf_eq_prime
∀ {G : Type u_1} [inst : AddMonoid G] {x : G} {p : ℕ} [hp : Fact (Nat.Prime p)], p • x = 0 → x ≠ 0 → addOrderOf x = pThe backward direction of addOrderOf_eq_prime_iff.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- addOrderOfstatement · cited by 208
- addOrderOf_eq_prime_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- add_notMem_of_exponent_twoproof · cited by 1
- addOrderOf_eq_two_iffproof · cited by 0