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<b>let </b><font color="Maroon" title="c1">z</font> be  <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">r</font> =  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c1">z</font>;<br/>
<b>set </b><font color="Maroon" title="c3">i</font> =  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">z</font>;<br/>
<b>thus </b><a NAME="E1:14"/>
( <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 <b>by </b><i><a class="ref" href="complex1.html#T12" target="_self" title="COMPLEX1:th.12">Th12</a></i>;<br/>

<b>assume </b><a NAME="E2:14"/>
0 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">z</font></span>)</span> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a> </span>)</span>
 ;<br/>

<a NAME="E3:14"/><b>then </b>
(  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 &amp;  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="complex1.html#T2" target="_self" title="COMPLEX1:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E4:14"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="complex1.html#T9" target="_self" title="COMPLEX1:th.9">Th9</a>, <a class="ref" href="complex1.html#T12" target="_self" title="COMPLEX1:th.12">Th12</a></i>;<br/>


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