∀ {α : Type u_6} {inst : NonUnitalNonAssocSemiring α} {toAddMonoidHom : α →+ α}
  {map_mul_left' : ∀ (a b : α), (↑toAddMonoidHom).toFun (a * b) = a * (↑toAddMonoidHom).toFun b}
  {map_mul_right' : ∀ (a b : α), (↑toAddMonoidHom).toFun (a * b) = (↑toAddMonoidHom).toFun a * b}
  {toAddMonoidHom_1 : α →+ α}
  {map_mul_left'_1 : ∀ (a b : α), (↑toAddMonoidHom_1).toFun (a * b) = a * (↑toAddMonoidHom_1).toFun b}
  {map_mul_right'_1 : ∀ (a b : α), (↑toAddMonoidHom_1).toFun (a * b) = (↑toAddMonoidHom_1).toFun a * b},
  { toAddMonoidHom := toAddMonoidHom, map_mul_left' := map_mul_left', map_mul_right' := map_mul_right' } =
      { toAddMonoidHom := toAddMonoidHom_1, map_mul_left' := map_mul_left'_1, map_mul_right' := map_mul_right'_1 } →
    toAddMonoidHom = toAddMonoidHom_1