English
For all s,t, permutations s ~ permutations t iff s ~ t; this is the symmetric form of the previous result.
Русский
Для любых s,t, permutations s ~ permutations t эквивалентно s ~ t; это симметричная форма предыдущей идеи.
LaTeX
$$$$\text{Permutations } s \sim \text{Permutations } t \iff s \sim t$$$$
Lean4
@[simp]
theorem perm_permutations_iff {s t : List α} : permutations s ~ permutations t ↔ s ~ t :=
⟨fun h => mem_permutations.1 <| h.mem_iff.1 <| mem_permutations.2 (Perm.refl _), Perm.permutations⟩