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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><b>that </b><br/><a NAME="E1:8"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green">E15</font></i>: 
 <a href="quin_1.html#K1" target="_self">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/>

<a NAME="E3:8"/><i><font color="Green">E16</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="quin_1.html#K1" target="_self">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a>  <a href="xcmplx_0.html#K4">-</a> 0
 
<b>by </b><i>, <a class="ref" href="real_2.html#T109">REAL_2:109</a></i>;<br/>
<a NAME="E4:8"/>
4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T134">XREAL_1:134</a></i>;<br/>
<a NAME="E5:8"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><a href="quin_1.html#K1" target="_self">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i>, <a class="ref" href="real_2.html#T126">REAL_2:126</a></i>;<br/>
<a NAME="E6:8"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quin_1.html#K1" target="_self">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T188">XCMPLX_1:188</a></i>;<br/>
<a NAME="E7:8"/><b>then </b><i><font color="Green">E17</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quin_1.html#K1" target="_self">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E8:8"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a>  <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/>
<a NAME="E9:8"/><b>then </b>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T133">XREAL_1:133</a></i>;<br/>
<a NAME="E10:8"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="quin_1.html#K1" target="_self">delta</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">a</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E11:8"/>
<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="xxreal_0.html#R1">&lt;=</a> 0
 <b>by </b><i>, </i>;<br/>


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