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<b>consider </b><font color="Maroon">a01</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a02</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">a03</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:65_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a01</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Maroon">a02</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Maroon">a03</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">a01</font> <a href="real_1.html#K3">+</a> <font color="Maroon">a02</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Maroon">a03</font> <a href="hidden.html#R1">=</a> 1 &amp; ( for <font color="Olive">b1</font>, <font color="Olive">b2</font>, <font color="Olive">b3</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b1</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Olive">b2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Olive">b3</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p3</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">b1</font> <a href="real_1.html#K3">+</a> <font color="Olive">b2</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">b3</font> <a href="hidden.html#R1">=</a> 1 holds <br/>( <font color="Olive">b1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a01</font> &amp; <font color="Olive">b2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a02</font> &amp; <font color="Olive">b3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a03</font> ) ) )
 <b>by </b><i>, </i>;<br/>
<b>thus </b><a NAME="E3:65_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">a2</font>, <font color="Olive">a3</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="real_1.html#K3">+</a> <font color="Olive">a2</font></span>)</span> <a href="real_1.html#K3">+</a> <font color="Olive">a3</font> <a href="hidden.html#R1">=</a> 1 &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K18">*</a> <font color="Maroon">p1</font></span>)</span> <a href="euclid.html#K17">+</a> <span class="p2">(<span class="default"><font color="Olive">a2</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p2</font></span>)</span></span>)</span> <a href="euclid.html#K17">+</a> <span class="p1">(<span class="default"><font color="Olive">a3</font> <a href="euclid.html#K18">*</a> <font color="Maroon">p3</font></span>)</span> )
 <b>by </b><i/>;<br/>


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