map_mk_ofList — Mathlib

English

Mapping preserves the monoid structure when applied to lists: map f g on the monoid element mk(ofList l) equals mk(ofList (l.map Sum.map f g)).

Русский

Отображение сохраняет структуру моноида на списках: map f g на элементе mk(ofList l) равно mk(ofList (l.map Sum.map f g)).

LaTeX

$$$\mathrm{map\, f\, g} \bigl(\mathrm{mk}(\mathrm{ofList}\ l)\bigr) = \mathrm{mk}\bigl(\mathrm{ofList}\ (l.map(\mathrm{Sum.map}\ f\ g))\bigr).$$$

Lean4

@[to_additive (attr := simp)]
theorem map_mk_ofList (f : M →* M') (g : N →* N') (l : List (M ⊕ N)) :
    map f g (mk (ofList l)) = mk (ofList (l.map (Sum.map f g))) :=
  rfl

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