Theorems · Theorem · group theory
IsAddTorsion.torsion_eq_top
∀ {G : Type u_1} [inst : AddCommMonoid G], IsAddTorsion G → AddCommMonoid.addTorsion G = ⊤The torsion additive submonoid of a torsion additive 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
- AddCommMonoid
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.
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement and proof · cited by 9,680
- AddSubmonoidstatement · cited by 1,178
- IsAddTorsionstatement and proof · cited by 42
- AddSubmonoid.extproof · cited by 32
- AddCommMonoid.addTorsionstatement and proof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- IsAddTorsion.torsionAddEquivproof · cited by 4
- IsAddTorsion.torsionAddEquiv_applystatement · cited by 1
- AddMonoid.IsTorsion.torsionAddEquiv_applystatement · cited by 0
- AddMonoid.IsTorsion.torsion_eq_topproof · cited by 0