Provide a mathematical proof. Thank you.

\f\f\f\fProvide a mathematical proof utilizing the following lemmas and theorems attached below Provide a prost Lemma 64: IF XI > y, and 21 > , then Xz 2z 57/55 Provide a proof Lemma 65: IF and NIN and NIN thenLemma 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