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<b>let </b><font color="Maroon">c<sub>1</sub></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<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">c<sub>1</sub></font>, <a href="numbers.html#K2">COMPLEX</a> ;<br/>







<b>assume </b><a NAME="E1:65"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="partfun1.html#V1">total</a> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a> )
 ;<br/>

<a NAME="E2:65"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E3:65"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:65"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K8">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T3" target="_self">Th3</a></i>;<br/>

<a NAME="E5:65"/>
<font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:65"><i><font color="Green">E48</font></i></a>, <a class="ref" href="cfunct_1.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E6:65"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:65"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K11">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T4" target="_self">Th4</a></i>;<br/>

<a NAME="E8:65"/>
<font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>4</sub></font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:65"><i><font color="Green">E48</font></i></a>, <a class="ref" href="cfunct_1.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E9:65"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E10:65"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="comseq_1.html#K3">(#)</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="complex1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self">Th5</a></i>;<br/>


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