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<b>let </b><font color="Maroon" title="c1">seq</font> be   <a href="comseq_1.html#NM1" title="COMSEQ_1:NM.1">Complex_Sequence</a>;<br/><b>let </b><font color="Maroon" title="c2">h1</font>, <font color="Maroon" title="c3">h2</font> be   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> , <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ;<br/>





<b>assume </b><a NAME="E1:28"/>
( <font color="Maroon" title="c2">h1</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> &amp; <font color="Maroon" title="c3">h2</font> is <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> )
 ;<br/>

<a NAME="E2:28"/><b>then </b>
<font color="Maroon" title="c2">h1</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <font color="Maroon" title="c3">h2</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" title="CFUNCT_1:th.70">CFUNCT_1:70</a></i>;<br/>
<a NAME="E3:28"/><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="c2">h1</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <font color="Maroon" title="c3">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a></i>;<br/>
<a NAME="E4:28"/><b>then </b>
<span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">h1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
<b>by </b><i><a class="ref" href="comseq_1.html#D2" title="COMSEQ_1:def.2">COMSEQ_1:def 2</a></i>;<br/>
<a NAME="E5:28"/><b>then </b><i><font color="Green" title="E21">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">seq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">h1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h2</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E6:28"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">h1</font> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <font color="Maroon" title="c3">h2</font></span>)</span> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">h1</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="comseq_1.html#K2" title="COMSEQ_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h2</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font></span>)</span>
 <b>by </b><i><a class="ref" href="cfcont_1.html#T18" target="_self" title="CFCONT_1:th.18">Th18</a></i>;<br/>

<b>thus </b><a NAME="E7:28"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">h1</font> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <font color="Maroon" title="c3">h2</font></span>)</span> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">h1</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="comseq_1.html#K6" title="COMSEQ_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h2</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font></span>)</span>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E5:28"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T18" target="_self" title="CFCONT_1:th.18">Th18</a></i>;<br/>

<b>thus </b><a NAME="E8:28"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">h1</font> <a href="comseq_1.html#K3" title="COMSEQ_1:func.3">(#)</a> <font color="Maroon" title="c3">h2</font></span>)</span> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">h1</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font></span>)</span> <a href="comseq_1.html#K3" title="COMSEQ_1:func.3">(#)</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h2</font> <a href="cfcont_1.html#K1" title="CFCONT_1:func.1">*</a> <font color="Maroon" title="c1">seq</font></span>)</span>
 <b>by </b><i><a class="txt" href="cfcont_1.html#E5:28"><i><font color="Green" title="E21">A1</font></i></a>, <a class="ref" href="cfcont_1.html#T18" target="_self" title="CFCONT_1:th.18">Th18</a></i>;<br/>


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