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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">x</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>assume </b><a NAME="E1:35"/><i><font color="Green">E34</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp;  <a href="quin_1.html#K1">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 ;<br/>

<b>assume </b><a NAME="E2:35"/>
 <a href="polyeq_1.html#K7" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,0,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E3:35"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0 <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E4:35"/>
<font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E5:35"/><b>then </b>
<font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/>
<a NAME="E6:35"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/>
<a NAME="E7:35"/>
<font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="power.html#K3">to_power</a> 1
 
<b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/>
<a NAME="E8:35"/><b>then </b>
<font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/>
<a NAME="E9:35"/><b>then </b>
<font color="Maroon">x</font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E10:35"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E11:35"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E12:35"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 or <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T6">XCMPLX_1:6</a></i>;<br/>
<a NAME="E13:35"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 or  <a href="polyeq_1.html#K3" target="_self">Polynom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 )
 
;<br/>
<b>hence </b><a NAME="E14:35"/>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">b</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> )
 <b>by </b><i>, </i>;<br/>


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