<?xml version="1.0"?>
<div class="add">

<a NAME="E1:19_1_1"/><i><font color="Green" title="E24">A2</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/>
<a NAME="E2:19_1_1"/><i><font color="Green" title="E25">A3</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
 
;<br/>
<a NAME="E3:19_1_1"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
 
<b>by </b><i><a class="txt" href="square_1.html#E85"><i><font color="Green" title="E15">Lm11</font></i></a></i>;<br/>
<a NAME="E4:19_1_1"/><b>then </b>
0 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">a</font>
 
<b>by </b><i><a class="txt" href="square_1.html#E1:19"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<a NAME="E5:19_1_1"/><b>then </b><i><font color="Green" title="E26">A4</font></i>: 
0 <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[ <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ] <b>means </b>( $1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 or $1 <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font> );<br/>
<b>defpred </b><font color="Maroon">S<sub>2</sub></font>[ <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ] <b>means </b>( 0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 &amp; <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  );<br/>
<div><i><font color="Green" title="E27">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:19_1_1_1"/><i><font color="Green" title="E28">A6</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">x</font>]
 <b>and </b><br/><a NAME="E2:19_1_1_1"/><i><font color="Green" title="E29">A7</font></i>: 
<font color="Maroon">S<sub>2</sub></font>[<font color="Maroon" title="c3">y</font>]
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 or  not <font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:19_1_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:19_1_1_1_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="txt" href="square_1.html#E2:19_1_1_1"><i><font color="Green" title="E29">A7</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:19_1_1_1_1_2"/>
not <font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:19_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">y</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_1"><i><font color="Green" title="E28">A6</font></i></a>, <a class="txt" href="square_1.html#E2:19_1_1_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E3:19_1_1_1_1_2"/>
<font color="Maroon" title="c2">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">y</font>
 <b>by </b><i><a class="txt" href="square_1.html#E2:19_1_1_1"><i><font color="Green" title="E29">A7</font></i></a>, <a class="ref" href="square_1.html#T78" target="_self" title="SQUARE_1:th.78">Th78</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c2">z</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E8:19_1_1"/><i><font color="Green" title="E28">A8</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x</font>] &amp; <font color="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b2">y</font>] holds <br/>( <font color="Olive" title="b1">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">z</font> &amp; <font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">y</font> )
 <b>from </b><i><a class="ref" href="square_1.html#S1" target="_self" title="SQUARE_1:sch.1">SQUARE_1:sch 1</a>(<a class="txt" href="square_1.html#E6:19_1_1"><i><font color="Green" title="E27">A5</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c2">z</font>
;<br/>

<b>thus </b><a NAME="E9:19_1_1"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="square_1.html#E1:19_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="square_1.html#E2:19_1_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="square_1.html#E5:19_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="square_1.html#E8:19_1_1"><i><font color="Green" title="E28">A8</font></i></a></i>;<br/>

<b>assume </b><a NAME="E10:19_1_1"/><i><font color="Green" title="E29">A9</font></i>: 
<font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1_1_2_1"/>
( <font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 or ( <font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">a</font> &amp; not <font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 ) or ( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  &amp; not <font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 ) )
 </span><b>by </b><i><a class="txt" href="square_1.html#E10:19_1_1"><i><font color="Green" title="E29">A9</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:19_1_1_2_1_1"/><i><font color="Green" title="E30">A10</font></i>: 
<font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0
 ;<br/><div class="add"><a NAME="E2:19_1_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="txt" href="square_1.html#E1:19"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="square_1.html#E1:19_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="square_1.html#E2:19_1_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="square_1.html#E5:19_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="square_1.html#E8:19_1_1"><i><font color="Green" title="E28">A8</font></i></a></i>;<br/><a NAME="E3:19_1_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><b>then consider </b><font color="Maroon" title="c3">c</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E5:19_1_1_2_1_1"/><i><font color="Green" title="E31">A11</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">c</font>
 <b>and </b><br/><a NAME="E6:19_1_1_2_1_1"/><i><font color="Green" title="E32">A12</font></i>: 
<font color="Maroon" title="c3">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="square_1.html#E10:19_1_1"><i><font color="Green" title="E29">A9</font></i></a>, <a class="txt" href="square_1.html#E92"><i><font color="Green" title="E19">Lm13</font></i></a></i>;<br/><b>thus </b><a NAME="E7:19_1_1_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="square_1.html#E1:19"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="square_1.html#E1:19_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="square_1.html#E2:19_1_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="square_1.html#E5:19_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="square_1.html#E8:19_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="square_1.html#E1:19_1_1_2_1_1"><i><font color="Green" title="E30">A10</font></i></a>, <a class="txt" href="square_1.html#E5:19_1_1_2_1_1"><i><font color="Green" title="E31">A11</font></i></a>, <a class="txt" href="square_1.html#E6:19_1_1_2_1_1"><i><font color="Green" title="E32">A12</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:19_1_1_2_1_2"/><i><font color="Green" title="E30">A13</font></i>: 
( <font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">a</font> &amp; not <font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 )
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c3">b</font> = <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>;<br/><a NAME="E2:19_1_1_2_1_2"/><i><font color="Green" title="E31">A14</font></i>: 
0 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><a NAME="E3:19_1_1_2_1_2"/><i><font color="Green" title="E32">A15</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_2"><i><font color="Green" title="E30">A13</font></i></a>, <a class="txt" href="square_1.html#E3"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><a NAME="E4:19_1_1_2_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <b>by </b><i><a class="txt" href="square_1.html#E2:19_1_1_2_1_2"><i><font color="Green" title="E31">A14</font></i></a>, <a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a></i>;<br/><b>then consider </b><font color="Maroon" title="c4">c</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><br/><a NAME="E6:19_1_1_2_1_2"/><i><font color="Green" title="E33">A16</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">c</font>
 <b>and </b><br/><a NAME="E7:19_1_1_2_1_2"/><i><font color="Green" title="E34">A17</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <b>by </b><i><a class="txt" href="square_1.html#E92"><i><font color="Green" title="E19">Lm13</font></i></a></i>;<br/><a NAME="E8:19_1_1_2_1_2"/><i><font color="Green" title="E35">A18</font></i>: 
2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_2"><i><font color="Green" title="E30">A13</font></i></a></i>;<br/><a NAME="E9:19_1_1_2_1_2"/><i><font color="Green" title="E36">A19</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_2"><i><font color="Green" title="E30">A13</font></i></a>, <a class="txt" href="square_1.html#E5"><i><font color="Green" title="E3">Lm3</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c5">eps</font> =  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>;<br/><a NAME="E10:19_1_1_2_1_2"/><i><font color="Green" title="E37">A20</font></i>: 
0 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><a NAME="E11:19_1_1_2_1_2"/>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_2"><i><font color="Green" title="E30">A13</font></i></a>, <a class="txt" href="square_1.html#E6"><i><font color="Green" title="E4">Lm4</font></i></a></i>;<br/><a NAME="E12:19_1_1_2_1_2"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E3:19_1_1_2_1_2"><i><font color="Green" title="E32">A15</font></i></a>, <a class="txt" href="square_1.html#E10:19_1_1_2_1_2"><i><font color="Green" title="E37">A20</font></i></a>, <a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a></i>;<br/><a NAME="E13:19_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E38">A21</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E6:19_1_1_2_1_2"><i><font color="Green" title="E33">A16</font></i></a>, <a class="txt" href="square_1.html#E34"><i><font color="Green" title="E9">Lm9</font></i></a></i>;<br/><a NAME="E14:19_1_1_2_1_2"/>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 2</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E33"><i><font color="Green" title="E8">Lm8</font></i></a></i>;<br/><a NAME="E15:19_1_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E9:19_1_1_2_1_2"><i><font color="Green" title="E36">A19</font></i></a>, <a class="ref" href="xreal_1.html#T66" title="XREAL_1:th.66">XREAL_1:66</a></i>;<br/><a NAME="E16:19_1_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T79" title="XCMPLX_1:th.79">XCMPLX_1:79</a></i>;<br/><a NAME="E17:19_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E39">A22</font></i>: 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <b>by </b><i><a class="txt" href="square_1.html#E8:19_1_1_2_1_2"><i><font color="Green" title="E35">A18</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E18:19_1_1_2_1_2"/>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="txt" href="square_1.html#E33"><i><font color="Green" title="E8">Lm8</font></i></a></i>;<br/><a NAME="E19:19_1_1_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">c</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
 <b>by </b><i><a class="txt" href="square_1.html#E13:19_1_1_2_1_2"><i><font color="Green" title="E38">A21</font></i></a>, <a class="ref" href="square_1.html#T77" target="_self" title="SQUARE_1:th.77">Th77</a></i>;<br/><a NAME="E20:19_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E40">A23</font></i>: 
<span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2
 <b>by </b><i><a class="txt" href="square_1.html#E7:19_1_1_2_1_2"><i><font color="Green" title="E34">A17</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E21:19_1_1_2_1_2"/><i><font color="Green" title="E41">A24</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E22:19_1_1_2_1_2"/><i><font color="Green" title="E42">A25</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p0">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E23:19_1_1_2_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E17:19_1_1_2_1_2"><i><font color="Green" title="E39">A22</font></i></a>, <a class="txt" href="square_1.html#E20:19_1_1_2_1_2"><i><font color="Green" title="E40">A23</font></i></a>, <a class="ref" href="xreal_1.html#T9" title="XREAL_1:th.9">XREAL_1:9</a></i>;<br/><a NAME="E24:19_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E43">A26</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="square_1.html#E21:19_1_1_2_1_2"><i><font color="Green" title="E41">A24</font></i></a>, <a class="txt" href="square_1.html#E22:19_1_1_2_1_2"><i><font color="Green" title="E42">A25</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E25:19_1_1_2_1_2"/>
<font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <font color="Maroon" title="c4">c</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">4 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E13:19_1_1_2_1_2"><i><font color="Green" title="E38">A21</font></i></a>, <a class="ref" href="xreal_1.html#T31" title="XREAL_1:th.31">XREAL_1:31</a></i>;<br/><b>hence </b><a NAME="E26:19_1_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="square_1.html#E1:19"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="square_1.html#E1:19_1_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="square_1.html#E2:19_1_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="square_1.html#E5:19_1_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="txt" href="square_1.html#E8:19_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="square_1.html#E24:19_1_1_2_1_2"><i><font color="Green" title="E43">A26</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1_2_1_3"><b>suppose </b></a><a NAME="E1:19_1_1_2_1_3"/><i><font color="Green" title="E30">A27</font></i>: 
( <font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  &amp; not <font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 0 )
 ;<br/><div class="add"><b>set </b><font color="Maroon" title="c3">b</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font>;<br/><a NAME="E2:19_1_1_2_1_3"/><i><font color="Green" title="E31">A28</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_3"><i><font color="Green" title="E30">A27</font></i></a>, <a class="txt" href="square_1.html#E6"><i><font color="Green" title="E4">Lm4</font></i></a></i>;<br/><a NAME="E3:19_1_1_2_1_3"/><i><font color="Green" title="E32">A29</font></i>: 
2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_3"><i><font color="Green" title="E30">A27</font></i></a></i>;<br/><a NAME="E4:19_1_1_2_1_3"/><i><font color="Green" title="E33">A30</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_3"><i><font color="Green" title="E30">A27</font></i></a>, <a class="txt" href="square_1.html#E3"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c4">eps</font> =  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font>;<br/><a NAME="E5:19_1_1_2_1_3"/><i><font color="Green" title="E34">A31</font></i>: 
0 <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 ;<br/><a NAME="E6:19_1_1_2_1_3"/>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_3"><i><font color="Green" title="E30">A27</font></i></a>, <a class="txt" href="square_1.html#E6"><i><font color="Green" title="E4">Lm4</font></i></a></i>;<br/><a NAME="E7:19_1_1_2_1_3"/><b>then </b>
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E4:19_1_1_2_1_3"><i><font color="Green" title="E33">A30</font></i></a>, <a class="txt" href="square_1.html#E5:19_1_1_2_1_3"><i><font color="Green" title="E34">A31</font></i></a>, <a class="ref" href="real_1.html#T73" title="REAL_1:th.73">REAL_1:73</a></i>;<br/><a NAME="E8:19_1_1_2_1_3"/><b>then </b><i><font color="Green" title="E35">A32</font></i>: 
0 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E1:19_1_1_2_1_3"><i><font color="Green" title="E30">A27</font></i></a>, <a class="txt" href="square_1.html#E34"><i><font color="Green" title="E9">Lm9</font></i></a></i>;<br/><a NAME="E9:19_1_1_2_1_3"/><i><font color="Green" title="E36">A33</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span>
 ;<br/><a NAME="E10:19_1_1_2_1_3"/><i><font color="Green" title="E37">A34</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p3">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p5">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E11:19_1_1_2_1_3"/>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E33"><i><font color="Green" title="E8">Lm8</font></i></a></i>;<br/><a NAME="E12:19_1_1_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E2:19_1_1_2_1_3"><i><font color="Green" title="E31">A28</font></i></a>, <a class="ref" href="xreal_1.html#T66" title="XREAL_1:th.66">XREAL_1:66</a></i>;<br/><a NAME="E13:19_1_1_2_1_3"/><b>then </b><i><font color="Green" title="E38">A35</font></i>: 
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="square_1.html#E3:19_1_1_2_1_3"><i><font color="Green" title="E32">A29</font></i></a>, <a class="ref" href="xcmplx_1.html#T88" title="XCMPLX_1:th.88">XCMPLX_1:88</a></i>;<br/><a NAME="E14:19_1_1_2_1_3"/>
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
 <b>by </b><i><a class="txt" href="square_1.html#E85"><i><font color="Green" title="E15">Lm11</font></i></a></i>;<br/><a NAME="E15:19_1_1_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 0
 <b>by </b><i><a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E16:19_1_1_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="txt" href="square_1.html#E13:19_1_1_2_1_3"><i><font color="Green" title="E38">A35</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E17:19_1_1_2_1_3"/><b>then </b><i><font color="Green" title="E39">A36</font></i>: 
<font color="Maroon" title="c1">a</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span></span>)</span> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
 <b>by </b><i><a class="txt" href="square_1.html#E9:19_1_1_2_1_3"><i><font color="Green" title="E36">A33</font></i></a>, <a class="txt" href="square_1.html#E10:19_1_1_2_1_3"><i><font color="Green" title="E37">A34</font></i></a>, <a class="ref" href="real_1.html#T92" title="REAL_1:th.92">REAL_1:92</a></i>;<br/><a NAME="E18:19_1_1_2_1_3"/>
 <a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p2">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E33"><i><font color="Green" title="E8">Lm8</font></i></a></i>;<br/><a NAME="E19:19_1_1_2_1_3"/><b>then </b><i><font color="Green" title="E40">A37</font></i>: 
0 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">z</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="square_1.html#E4"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/><a NAME="E20:19_1_1_2_1_3"/>
<font color="Maroon" title="c2">z</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><a href="xxreal_0.html#K3" title="XXREAL_0:func.3">min</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c2">z</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c1">a</font></span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">z</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">z</font></span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">z</font>
 <b>by </b><i><a class="txt" href="square_1.html#E8:19_1_1_2_1_3"><i><font color="Green" title="E35">A32</font></i></a>, <a class="txt" href="square_1.html#E32"><i><font color="Green" title="E7">Lm7</font></i></a></i>;<br/><b>hence </b><a NAME="E21:19_1_1_2_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="square_1.html#E8:19_1_1"><i><font color="Green" title="E28">A8</font></i></a>, <a class="txt" href="square_1.html#E17:19_1_1_2_1_3"><i><font color="Green" title="E39">A36</font></i></a>, <a class="txt" href="square_1.html#E19:19_1_1_2_1_3"><i><font color="Green" title="E40">A37</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E12:19_1_1"/>
contradiction
 ;<br/>


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