Theorem 1.1.1: For any regular expressions _, _ and _,
(i) _ + _ ___ + _ ,
(ii) (_ + _) + _ ____ + (_ + _),
(iii) __+ _ _ _ + _ ____ ,
(iv) (_ _) _ _ __(____ ),
(v) _(_ + _) _ ___ + _ _ ,
(vi) (_ + _) _ _ _ _ + ___ ,
(vii) _ _ _ _ _ ____ ,
(viii) _ _ _ _ _ _ _,
(ix) _* _ _ ,
(x) (_ + _)* _ _*,
(xi) _(_ _)* _ (___ )* _ ,
(xii) (_*)* __ _*,
(xiii) (_* _*)* _ (_ + _)*,
(xiv) (_ _*)* ____ + _(_ + _)*.
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