∀ {k : Type u₁} {G : Type u₂} [inst : Semiring k] [inst_1 : Add G] [inst_2 : DecidableEq G] (f : AddMonoidAlgebra k G)
  {r : k},
  (∀ (y : k), y * r = 0 ↔ y = 0) →
    ∀ {x : G},
      IsAddRightRegular x → (f * AddMonoidAlgebra.single x r).support = Finset.image (fun x_1 => x_1 + x) f.support