derangementsCongr — Mathlib

English

Derangements are preserved under equivalences of the underlying set: if α ≃ β, then derangements α ≃ derangements β.

Русский

Деранджменты сохраняются при эквивалентности базовых множеств: если α ≃ β, то дерangements α ≃ дерangements β.

LaTeX

$$$\text{derangements}(\alpha) \cong \text{derangements}(\beta)$ via the given equivalence$$

Lean4

/-- If `α` is equivalent to `β`, then `derangements α` is equivalent to `derangements β`. -/
def derangementsCongr (e : α ≃ β) : derangements α ≃ derangements β :=
  e.permCongr.subtypeEquiv fun {f} =>
    e.forall_congr <| by intro b; simp only [ne_eq, permCongr_apply, symm_apply_apply, EmbeddingLike.apply_eq_iff_eq]

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