instCommGroup — Mathlib

English

If Y is CommGroup, LocallyConstant X Y inherits a CommGroup structure with pointwise commutativity of multiplication.

Русский

Если Y — комм-группа, LocallyConstant X Y наследует CommGroup с точной антифункцией умножения.

LaTeX

$$$\forall f,g:\mathrm{LocallyConstant}(X,Y),\; (f\cdot g)(x) = (g\cdot f)(x).$$$

Lean4

@[to_additive]
instance [CommGroup Y] : CommGroup (LocallyConstant X Y) :=
  Function.Injective.commGroup DFunLike.coe DFunLike.coe_injective' rfl (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)
    (fun _ _ => rfl) (fun _ _ => rfl)

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