Mathlib Map

Theorems · Theorem · group theory

ExponentExists.isAddTorsion

∀ {G : Type u_1} [inst : AddGroup G], AddMonoid.ExponentExists G → IsAddTorsion G

If a group exponent exists, the additive group is torsion.

Defined in
Mathlib.GroupTheory.Torsion
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
AddGroup
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isAddTorsion_of_finite · cited by 3isAddTorsion_of_finiteExponentExists.is_add_torsion · cited by 0ExponentExists.is_add_tor…AddGroup · cited by 4410AddGroupIsAddTorsion · cited by 42IsAddTorsionisOfFinAddOrder_iff_nsmul_eq_zero · cited by 27isOfFinAddOrder_iff_nsmul…AddMonoid.ExponentExists · cited by 17AddMonoid.ExponentExistsExponentExists.isAddTorsionCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.