of_not_isCyclic — Mathlib

English

Let G be a group. If G is not cyclic, then G is nontrivial.

Русский

Пусть G — группа. Если G не циклична, то она неп trivиальна.

LaTeX

$$$\\neg IsCyclic(\\alpha) \\Rightarrow Nontrivial(\\alpha)$$$

Lean4

/-- A non-cyclic multiplicative group is non-trivial. -/
@[to_additive /-- A non-cyclic additive group is non-trivial. -/
    ]
theorem of_not_isCyclic (nc : ¬IsCyclic α) : Nontrivial α :=
  by
  contrapose! nc
  exact @isCyclic_of_subsingleton _ _ nc

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