Question 1086326
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From Wikipedia article   https://en.wikipedia.org/wiki/Lemma_(mathematics)

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    In mathematics, a  lemma (a "helping theorem") is a proved proposition which is used as a stepping stone 
    to a larger result rather than as a statement of interest by itself. 
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<pre>
<U>Lemma 1</U>.  

    If {{{a/b}}} = {{{c/d}}} then {{{(a + c)/(b+d)}}} = {{{a/b}}} = {{{c/d}}}.


        <U>Proof</U>. Let {{{a/b}}} = {{{c/d}}} = k. Then

               a = b*k,  c = d*k  and  {{{(a + c)/(b+d)}}} = {{{(bk + dk)/(b + d)}}} = {{{((b+d)*k)/(b+d)}}} = k = {{{a/b}}} = {{{c/d}}}.

        The lemma is proved.



<U>Lemma 2</U>. 

    If {{{a/b}}} = {{{c/d}}} = {{{e/f}}}  then  {{{a^3/b^3}}} = {{{c^3/d^3}}} = {{{e^3/v^3}}}.


       The proof is obvious.



<U>Major statement</U>.  {{{(a^3+c^3+e^3)/(b^3+d^3+f^3)}}} = {{{(a/b)^3}}}.


    <U>Proof</U>. It follows IMMEDIATELY Lemma 1  and  Lemma 2.
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