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Theorems · Theorem · group theory

IsAddTorsionFree.of_not_isOfFinAddOrder

∀ {G : Type u_1} [inst : AddCommGroup G], (∀ ⦃a : G⦄, a ≠ 0 → ¬IsOfFinAddOrder a) → IsAddTorsionFree G

Alias of the reverse direction of isAddTorsionFree_iff_not_isOfFinAddOrder.

Defined in
Mathlib.GroupTheory.OrderOfElement
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0 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroup
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AddCommGroup · cited by 12871AddCommGroupIsAddTorsionFree · cited by 155IsAddTorsionFreeIsOfFinAddOrder · cited by 105IsOfFinAddOrderisAddTorsionFree_iff_not_isOfFinAddOrder · cited by 4isAddTorsionFree_iff_not_…IsAddTorsionFree.of_not_isOfF…CITED BYCITES

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