not_isTorsion_of_isMulTorsionFree

English

A nontrivial torsion abelian group is not torsion-free.

Русский

Непустая торовая абелевая группа не тождественно свободна от торсионности.

LaTeX

$$Not (IsMulTorsionFree G) given (IsTorsion G) and Nontrivial G$$

Lean4

/-- A nontrivial torsion-free abelian group is not torsion. -/
@[to_additive /-- A nontrivial additive torsion-free abelian group is not torsion. -/
    ]
theorem not_isTorsion_of_isMulTorsionFree [Nontrivial G] [IsMulTorsionFree G] : ¬IsTorsion G :=
  (not_isMulTorsionFree_of_isTorsion · ‹_›)

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