Theorems · Theorem · group theory
AddMonoid.exponent_ne_zero_iff_range_addOrderOf_finite
∀ {G : Type u} [inst : AddMonoid G],
(∀ (g : G), 0 < addOrderOf g) → (AddMonoid.exponent G ≠ 0 ↔ (Set.range addOrderOf).Finite)- Defined in
- Mathlib.GroupTheory.Exponent
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- AddMonoidstatement and proof · cited by 2,864
- Finset.prodproof · cited by 2,356
- Set.Finitestatement and proof · cited by 1,814
- LT.lt.ne'proof · cited by 1,417
- Set.mem_range_selfproof · cited by 328
- addOrderOfstatement and proof · cited by 208
- Finset.mem_coeproof · cited by 91
- AddMonoid.exponentstatement and proof · cited by 70
Cited by3
Results whose statement or proof uses this declaration.
- AddMonoid.exponent_eq_zero_iff_range_addOrderOf_infiniteproof · cited by 1
- AddMonoid.exists_addOrderOf_eq_exponentproof · cited by 1
- IsAddTorsion.exponentExistsproof · cited by 0