Theorems · Theorem · group theory
not_isAddTorsionFree_iff_isOfFinAddOrder
∀ {G : Type u_1} [inst : AddCommGroup G], ¬IsAddTorsionFree G ↔ ∃ a, a ≠ 0 ∧ IsOfFinAddOrder a- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 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.
Cites4
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
- IsAddTorsionFreestatement · cited by 155
- IsOfFinAddOrderstatement and proof · cited by 105
- isAddTorsionFree_iff_not_isOfFinAddOrderproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- not_isAddTorsionFree_of_isAddTorsionproof · cited by 2