Provide a mathematical proof. Thank you.

\f\f\f\fProvide a mathematical proof, utilize the following lemmas and theorems attatched below Provide a proout theorem 61 : Distributive law For any fraction XI, y1, and 21 , we have ' y ' + NIN X. ZI 2 2 ' XZZZ Provide a proof : Lemma 63: IF X:ZI V y, 2 1 of XiZI 2 y, 21 of X2 22 42 22 X2 22 y, 22 x z Z z then 9 1 or LA or XI Ly .Lemma 66. If -> 1 and 21 > 1 then *1 Z1 , Vil 2 2 -U2 X 2 Z2 - V/2 U2 Theorem 67. If - and 1 are any given fractions, then the equivalence -1 - 21 1 has a * 2 y2 *2 V/2 U2 solution -1 in the set of fractions. If - and - are any two solutions then ~- V 2 W 2 V 2 W 2