Theorems · Theorem · group theory
AddCommGroup.torsion_eq_torsion_addSubmonoid
∀ (G : Type u_1) [inst : AddCommGroup G], AddCommMonoid.addTorsion G = (AddCommGroup.torsion G).toAddSubmonoid
The torsion additive submonoid of an abelian group equals the torsion additive subgroup as an additive submonoid.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- AddSubmonoidstatement · cited by 1,178
- AddSubgroup.toAddSubmonoidstatement · cited by 91
- AddCommGroup.torsionstatement · cited by 18
- AddCommMonoid.addTorsionstatement · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- AddCommGroup.add_torsion_eq_add_torsion_submonoidproof · cited by 0