English
Mapping preserves the mk construction: map f on mk m hc equals mk of the mapped multiset.
Русский
Отображение сохраняет построение mk: map f на mk m hc равно mk картырованного множества.
LaTeX
$$$\\forall f : \\alpha \\to \\beta, \\forall m : \\mathrm{Multiset}(\\alpha), \\forall hc, \\mathrm{Sym.map}(f)(\\mathrm{Sym.mk}(m,hc)) = \\mathrm{Sym.mk}(m.map f, (\\text{proof})).$$$
Lean4
@[simp]
theorem map_mk {f : α → β} {m : Multiset α} {hc : Multiset.card m = n} :
map f (mk m hc) = mk (m.map f) (by simp [hc]) :=
rfl