Cartesian Product Distributes over Set Difference

Theorem
Cartesian product is distributive over set difference:


 * $(1): \quad S \times \paren {T_1 \setminus T_2} = \paren {S \times T_1} \setminus \paren {S \times T_2}$
 * $(2): \quad \paren {T_1 \setminus T_2} \times S = \paren {T_1 \times S} \setminus \paren {T_2 \times S}$