Theorems · Theorem · group theory
AddMonoid.exponent_eq_zero_addOrder_zero
∀ {G : Type u} [inst : AddMonoid G] {g : G}, addOrderOf g = 0 → AddMonoid.exponent G = 0- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- LT.lt.ne'proof · cited by 1,417
- addOrderOfstatement and proof · cited by 208
- AddMonoid.exponentstatement · cited by 70
- AddMonoid.ExponentExistsproof · cited by 17
- AddMonoid.exponent_eq_zero_iffproof · cited by 5
- AddMonoid.ExponentExists.addOrderOf_posproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoid.exponent_eq_iSup_addOrderOf'proof · cited by 0
- IsAddCyclic.exponent_eq_zero_of_infiniteproof · cited by 0