Theorems · Definition · group theory
IsAddTorsion.torsionAddEquiv
{G : Type u_1} → [inst : AddCommMonoid G] → IsAddTorsion G → ↥(AddCommMonoid.addTorsion G) ≃+ GA torsion additive monoid is isomorphic to its torsion additive submonoid.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement · cited by 1,178
- AddEquivstatement · cited by 1,087
- AddEquiv.transproof · cited by 53
- IsAddTorsionstatement and proof · cited by 42
- AddCommMonoid.addTorsionstatement · cited by 12
- AddSubmonoid.topEquivproof · cited by 4
- IsAddTorsion.torsion_eq_topproof · cited by 3
- AddEquiv.addSubmonoidCongrproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- IsAddTorsion.torsionAddEquiv_applystatement and proof · cited by 1
- IsAddTorsion.torsionAddEquiv_symm_apply_coestatement and proof · cited by 1
- AddMonoid.IsTorsion.torsionAddEquivproof · cited by 0
- AddMonoid.IsTorsion.torsionAddEquiv_applystatement · cited by 0
- AddMonoid.IsTorsion.torsionAddEquiv_symm_apply_coestatement · cited by 0
- AddCommMonoid.Torsion.ofTorsionproof · cited by 0