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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:5_1_1_1"/>
( <font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  or  not <font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_1_1"><b>suppose </b></a><a NAME="E1:5_1_1_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ;<br/><div class="add"><a NAME="E2:5_1_1_1_1"/><b>then </b>
 <a href="complex1.html#K1" title="COMPLEX1:func.1">Re</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z</font>
 <b>by </b><i><a class="ref" href="complex1.html#D2" target="_self" title="COMPLEX1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E3:5_1_1_1_1"/>
 <a href="complex1.html#K1" title="COMPLEX1:func.1">Re</a> <font color="Maroon" title="c1">z</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 <b>by </b><i><a class="txt" href="complex1.html#E1:5_1_1_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="5_1_1_1_2"><b>suppose </b></a><a NAME="E1:5_1_1_1_2"/>
not <font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of 2, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E3:5_1_1_1_2"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font>
 <b>and </b><br/><a NAME="E4:5_1_1_1_2"/><i><font color="Green" title="E6">A2</font></i>: 
 <a href="complex1.html#K1" title="COMPLEX1:func.1">Re</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="complex1.html#D2" target="_self" title="COMPLEX1:def.2">Def2</a></i>;<br/><a NAME="E5:5_1_1_1_2"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 2
 <b>by </b><i><a class="txt" href="complex1.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><a NAME="E6:5_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> 
 <b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/><b>hence </b><a NAME="E7:5_1_1_1_2"/>
 <a href="complex1.html#K1" title="COMPLEX1:func.1">Re</a> <font color="Maroon" title="c1">z</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 <b>by </b><i><a class="txt" href="complex1.html#E4:5_1_1_1_2"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="xreal_0.html#D1" title="XREAL_0:def.1">XREAL_0:def 1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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