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<b>let </b><font color="Maroon" title="c1">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">c</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">C</font>;<br/><b>let </b><font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Maroon" title="c1">C</font>, <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>







<b>assume </b><a NAME="E1:65"/><i><font color="Green" title="E48">A1</font></i>: 
( <font color="Maroon" title="c3">f1</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <font color="Maroon" title="c4">f2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> )
 ;<br/>

<a NAME="E2:65"/><b>then </b>
<font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <font color="Maroon" title="c4">f2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="ref" href="cfunct_1.html#T70" target="_self" title="CFUNCT_1:th.70">Th70</a></i>;<br/>
<a NAME="E3:65"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:65"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="complex1.html#K8" title="COMPLEX1:func.8">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T3" target="_self" title="CFUNCT_1:th.3">Th3</a></i>;<br/>

<a NAME="E5:65"/>
<font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c4">f2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:65"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="cfunct_1.html#T70" target="_self" title="CFUNCT_1:th.70">Th70</a></i>;<br/>
<a NAME="E6:65"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:65"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T4" target="_self" title="CFUNCT_1:th.4">Th4</a></i>;<br/>

<a NAME="E8:65"/>
<font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K3" title="COMSEQ_1:func.3">(#)</a> <font color="Maroon" title="c4">f2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>
 
<b>by </b><i><a class="txt" href="cfunct_1.html#E1:65"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="cfunct_1.html#T70" target="_self" title="CFUNCT_1:th.70">Th70</a></i>;<br/>
<a NAME="E9:65"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K3" title="COMSEQ_1:func.3">(#)</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E10:65"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="comseq_1.html#K3" title="COMSEQ_1:func.3">(#)</a> <font color="Maroon" title="c4">f2</font></span>)</span> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font></span>)</span> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f2</font> <a href="finseq_4.html#K4" title="FINSEQ_4:func.4">/.</a> <font color="Maroon" title="c2">c</font></span>)</span>
 <b>by </b><i><a class="ref" href="cfunct_1.html#T5" target="_self" title="CFUNCT_1:th.5">Th5</a></i>;<br/>


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