instNonUnitalSemiring — Mathlib

English

If Y is a NonUnitalSemiring, LocallyConstant X Y inherits a NonUnitalSemiring structure with pointwise addition and multiplication.

Русский

Если Y — немономоидная полусемирия, LocallyConstant X Y наследует такую структуру по точкам.

LaTeX

$$$\text{LocallyConstant}(X,Y)\text{ is a NonUnitalSemiring with } (f+g)(x)=f(x)+g(x), (f\cdot g)(x)=f(x)g(x).$$$

Lean4

instance [NonUnitalSemiring Y] : NonUnitalSemiring (LocallyConstant X Y) :=
  Function.Injective.nonUnitalSemiring DFunLike.coe DFunLike.coe_injective' rfl (fun _ _ => rfl) (fun _ _ => rfl)
    (fun _ _ => rfl)

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