reindex — Mathlib

English

Flattening n copies of a cyclically reduced word preserves cyclically reduced property.

Русский

Свертка n копий циклически сокращенного слова сохраняет цикличность.

LaTeX

$$$$ \\forall n, \\mathrm{IsCyclicallyReduced}(\\mathrm{List.flatten}(\\mathrm{List.replicate} \\ n \\ L)). $$$$

Lean4

/-- Reindex a free group basis through a bijection of the indexing sets. -/
protected def reindex (b : FreeGroupBasis ι G) (e : ι ≃ ι') : FreeGroupBasis ι' G :=
  ofRepr (b.repr.trans (FreeGroup.freeGroupCongr e))

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