Theorems · Theorem · group theory
isAddTorsionFree_iff_not_isOfFinAddOrder
∀ {G : Type u_1} [inst : AddCommGroup G], IsAddTorsionFree G ↔ ∀ ⦃a : G⦄, a ≠ 0 → ¬IsOfFinAddOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 22 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.
Cites9
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
- sub_eq_zeroproof · cited by 407
- IsAddTorsionFreestatement and proof · cited by 155
- Ne.bot_ltproof · cited by 116
- IsOfFinAddOrderstatement and proof · cited by 105
- of_not_notproof · cited by 51
- isOfFinAddOrder_iff_nsmul_eq_zeroproof · cited by 27
- not_isOfFinAddOrder_of_isAddTorsionFreeproof · cited by 7
- nsmul_subproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- not_isAddTorsionFree_iff_isOfFinAddOrderproof · cited by 1
- AddCommGroup.isAddTorsionFree_iff_torsion_eq_botproof · cited by 0
- IsAddTorsionFree.of_not_isOfFinAddOrderproof · cited by 0
- AddMonoid.minOrder_eq_top_iffproof · cited by 0