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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>











<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 3</span>)</span><b> such that </b><br/><a NAME="E2:31"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="euclid_5.html#K4" target="_self">]|</a></span>
 ;<br/>
<a NAME="E3:31"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>7</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="euclid_5.html#E2:31"><i><font color="Green">E23</font></i></a>, <a class="ref" href="euclid_5.html#T2" target="_self">Th2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 3</span>)</span><b> such that </b><br/><a NAME="E5:31"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="euclid_5.html#K4" target="_self">]|</a></span>
 ;<br/>
<a NAME="E6:31"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="euclid_5.html#K1" target="_self">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="euclid_5.html#K2" target="_self">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="euclid_5.html#K3" target="_self">`3</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="euclid_5.html#E5:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="euclid_5.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E7:31"/>
<span class="p1"><a href="euclid_2.html#K2">|(</a><span class="default"><span class="p2"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="euclid_5.html#K4" target="_self">]|</a></span>,<span class="p2"><a href="euclid_5.html#K4" target="_self">|[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="euclid_5.html#K4" target="_self">]|</a></span></span><a href="euclid_2.html#K2">)|</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="euclid_5.html#E2:31"><i><font color="Green">E23</font></i></a>, <a class="txt" href="euclid_5.html#E3:31"><i><font color="Green">E24</font></i></a>, <a class="txt" href="euclid_5.html#E5:31"><i><font color="Green">E25</font></i></a>, <a class="ref" href="euclid_5.html#T29" target="_self">Th29</a></i>;<br/>


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