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<b>let </b><font color="Maroon">seq</font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/><b>let </b><font color="Maroon">h1</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">h2</font> be   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="numbers.html#K1">REAL</a> , <a href="numbers.html#K1">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:30"/>
( <font color="Maroon">h1</font> is <a href="partfun1.html#V1">total</a> &amp; <font color="Maroon">h2</font> is <a href="partfun1.html#V1">total</a> )
 ;<br/>

<a NAME="E2:30"/><b>then </b>
<font color="Maroon">h1</font> <a href="seq_1.html#K6">+</a> <font color="Maroon">h2</font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="rfunct_1.html#T66">RFUNCT_1:66</a></i>;<br/>
<a NAME="E3:30"/><b>then </b>
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="seq_1.html#K6">+</a> <font color="Maroon">h2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<a NAME="E4:30"/><b>then </b>
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K1">REAL</a> 
 
<b>by </b><i><a class="ref" href="seq_1.html#D3">SEQ_1:def 3</a></i>;<br/>
<a NAME="E5:30"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">seq</font> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">h2</font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E6:30"/>
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="seq_1.html#K6">+</a> <font color="Maroon">h2</font></span>)</span> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E7:30"/>
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="seq_1.html#K7">-</a> <font color="Maroon">h2</font></span>)</span> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E8:30"/>
<span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="seq_1.html#K8">(#)</a> <font color="Maroon">h2</font></span>)</span> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">h1</font> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span> <a href="seq_1.html#K11">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="rfunct_2.html#K1" target="_self">*</a> <font color="Maroon">seq</font></span>)</span>
 <b>by </b><i>, </i>;<br/>


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