| (1) | $G = (X, +)$ is a D263: Groupoid |
| (2) | $H = (X, +)$ is a D263: Groupoid |
| (3) | The D20: Enclosed binary operation $\times$ is a D557: Distributive binary operation over $+$ |
| (1) | $G = (X, +)$ is a D263: Groupoid |
| (2) | $H = (X, +)$ is a D263: Groupoid |
| (3) | The D20: Enclosed binary operation $\times$ is a D557: Distributive binary operation over $+$ |