Commute.isNilpotent_add

theorem Commute.isNilpotent_add : ∀ {R : Type u_1} {x y : R} [inst : Semiring R], Commute x y → IsNilpotent x → IsNilpotent y → IsNilpotent (x + y)

The theorem `Commute.isNilpotent_add` states that for any type `R` that behaves as a semiring, given two elements `x` and `y` of this type, if `x` and `y` commute (meaning `x * y = y * x`), and if both `x` and `y` are nilpotent (meaning there exists a natural number `n` such that `x^n = 0` and `y^n = 0` respectively), then their sum `x + y` is also nilpotent.

More concisely: If `R` is a semiring, `x` and `y` are commuting nilpotent elements of `R`, then `x + y` is nilpotent.