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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:24_1_1_1"/>
( <font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font> or  not <font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_1"><b>suppose </b></a><a NAME="E1:24_1_1_1_1"/>
<font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font>
 ;<br/><div class="add"><a NAME="E2:24_1_1_1_1"/><b>then </b><i><font color="Green" title="E7">A1</font></i>: 
<font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">s</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E3:24_1_1_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">s</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 <b>by </b><i><a class="ref" href="valued_0.html#D1" title="VALUED_0:def.1">VALUED_0:def 1</a></i>;<br/><b>hence </b><a NAME="E4:24_1_1_1_1"/>
<font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 <b>by </b><i><a class="txt" href="matrix_5.html#E2:24_1_1_1_1"><i><font color="Green" title="E7">A1</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="24_1_1_1_2"><b>suppose </b></a><a NAME="E1:24_1_1_1_2"/>
not <font color="Maroon" title="c2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">s</font>
 ;<br/><div class="add"><a NAME="E2:24_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> 
 <b>by </b><i><a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/><b>hence </b><a NAME="E3:24_1_1_1_2"/>
<font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">k</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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