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<b>let </b><font color="Maroon">C</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/><b>let </b><font color="Maroon">f2</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/>







<b>assume </b><a NAME="E1:69"/>
( <font color="Maroon">f1</font> is <a href="partfun1.html#V1">total</a> &amp; <font color="Maroon">f2</font> <a href="cfunct_1.html#K2" target="_self">^</a>  is <a href="partfun1.html#V1">total</a> )
 ;<br/>

<a NAME="E2:69"/><b>then </b>
( <font color="Maroon">f1</font> is <a href="partfun1.html#V1">total</a> &amp; <font color="Maroon">f2</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="complex1.html#K5">0c</a> </span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">f2</font> is <a href="partfun1.html#V1">total</a> )
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E12"><i><font color="Green">Lemma46</font></i></a></i>;<br/>
<a NAME="E3:69"/><b>then </b>
<font color="Maroon">f1</font> <a href="cfunct_1.html#K1" target="_self">/</a> <font color="Maroon">f2</font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E4:69"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="cfunct_1.html#K1" target="_self">/</a> <font color="Maroon">f2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:69"/>
<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="cfunct_1.html#K1" target="_self">/</a> <font color="Maroon">f2</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span> <a href="complex1.html#K12">"</a> </span>)</span>
 <b>by </b><i/>;<br/>


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