Theorems · Theorem · group theory
IsMulTorsion.torsion_eq_top
∀ {G : Type u_1} [inst : CommMonoid G], IsMulTorsion G → CommMonoid.torsion G = ⊤The torsion submonoid of a torsion monoid is ⊤.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Submonoidstatement · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Submonoid.extproof · cited by 48
- IsMulTorsionstatement and proof · cited by 35
- CommMonoid.torsionstatement and proof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- IsMulTorsion.torsionMulEquivproof · cited by 4
- IsMulTorsion.torsionMulEquiv_applystatement · cited by 1
- Monoid.IsTorsion.torsion_eq_topproof · cited by 0
- Monoid.IsTorsion.torsionMulEquiv_applystatement · cited by 0