English
Let X be a topological space and Y a type equipped with a nonunital ring structure. Then LocallyConstant(X, Y) carries a natural pointwise nonunital ring structure, i.e., (f + g)(x) = f(x) + g(x) and (f · g)(x) = f(x) · g(x) with (0)(x) = 0.
Русский
Пусть X — топологическое пространство, Y — множество с неполным кольцом. Тогда множество LocallyConstant(X, Y) naturally наследует скалярно-по точкам структуру неединого кольца: (f + g)(x) = f(x) + g(x), (f · g)(x) = f(x) · g(x), (0)(x) = 0.
LaTeX
$$$\operatorname{NonUnitalRing}(\operatorname{LocallyConstant}(X,Y))$$$
Lean4
instance [NonUnitalRing Y] : NonUnitalRing (LocallyConstant X Y) :=
Function.Injective.nonUnitalRing DFunLike.coe DFunLike.coe_injective' rfl (fun _ _ => rfl) (fun _ _ => rfl)
(fun _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl)
