Theorems · Theorem · group theory
not_isAddTorsionFree_of_isAddTorsion
∀ {G : Type u_1} [inst : AddCommGroup G] [Nontrivial G], IsAddTorsion G → ¬IsAddTorsionFree GA nontrivial torsion additive abelian group is not torsion-free.
- Defined in
- Mathlib.GroupTheory.Torsion
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Nontrivialstatement and proof · cited by 2,416
- IsAddTorsionFreestatement · cited by 155
- IsOfFinAddOrderproof · cited by 105
- exists_neproof · cited by 101
- IsAddTorsionstatement and proof · cited by 42
- not_isAddTorsionFree_iff_isOfFinAddOrderproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- not_isAddTorsion_of_isAddTorsionFreeproof · cited by 1
- not_isAddTorsionFree_of_isTorsionproof · cited by 0