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<b>let </b><font color="Maroon" title="c1">f</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:73_1"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c1">f</font> is <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>
 ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:73_1_1"/>
( <font color="Maroon" title="c2">x</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">f</font> or  not <font color="Maroon" title="c2">x</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">f</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_1"><b>suppose </b></a><a NAME="E1:73_1_1_1"/>
<font color="Maroon" title="c2">x</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">f</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:73_1_1_1"/>
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>
 <b>by </b><i><a class="txt" href="valued_0.html#E1:73_1"><i><font color="Green" title="E20">A1</font></i></a>, <a class="ref" href="valued_0.html#D7" target="_self" title="VALUED_0:def.7">Def7</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="73_1_1_2"><b>suppose </b></a><a NAME="E1:73_1_1_2"/>
not <font color="Maroon" title="c2">x</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">f</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:73_1_1_2"/>
<font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</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/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:73"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds  <font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>
 ;<br/>

<a NAME="E3:73"/><b>then </b>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</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">f</font> holds <br/><font color="Maroon" title="c1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> is <a href="xcmplx_0.html#V1" title="XCMPLX_0:attr.1">complex</a>
 
;<br/>
<b>hence </b><a NAME="E4:73"/>
<font color="Maroon" title="c1">f</font> is <a href="valued_0.html#V1" title="VALUED_0:attr.1">complex-valued</a>
 <b>by </b><i><a class="ref" href="valued_0.html#D7" target="_self" title="VALUED_0:def.7">Def7</a></i>;<br/>


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