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<b>let </b><font color="Maroon">IT</font> be   <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>, <a href="numbers.html#K1">REAL</a> ;<br/>

<b>thus </b><a NAME="E1:26_1_1"/>
( <font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="comseq_1.html#K9" target="_self">|.</a><span class="default"><font color="Maroon">seq</font></span><a href="comseq_1.html#K9" target="_self">.|</a></span> implies (  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> &amp; ( for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds  <font color="Maroon">IT</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="funct_2.html#K3">.</a> <font color="Olive">c</font></span>)</span></span><a href="complex1.html#K17">.|</a></span> ) ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:26_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="comseq_1.html#K9" target="_self">|.</a><span class="default"><font color="Maroon">seq</font></span><a href="comseq_1.html#K9" target="_self">.|</a></span>
 ;<br/>

<b>hence </b><i><font color="Green">E33</font></i>:  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> = 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">seq</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">C</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/><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/>

<a NAME="E3:26_1_1_1"/>
<font color="Maroon">seq</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T22">FINSEQ_4:22</a></i>;<br/>
<b>hence </b><a NAME="E4:26_1_1_1"/>
<font color="Maroon">IT</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>

<b>assume </b><b>that </b><br/><a NAME="E2:26_1_1"/><i><font color="Green">E34</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font>
 <b>and </b><br/><a NAME="E3:26_1_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds  <font color="Maroon">IT</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="funct_2.html#K3">.</a> <font color="Olive">c</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 ;<br/>

<a NAME="E4:26_1_1"/><i><font color="Green">E36</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">seq</font>
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:26_1_1"/>
for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>  st <font color="Olive">c</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font> holds <br/><font color="Maroon">IT</font> <a href="seq_1.html#K2">.</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">c</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1_1_2"><b>proof </b></a><div class="add">

<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>assume </b><a NAME="E1:26_1_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">IT</font>
 ;<br/>

<a NAME="E2:26_1_1_2"/>
<font color="Maroon">seq</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">seq</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c</font>
 
<b>by </b><i><a class="ref" href="finseq_4.html#T22">FINSEQ_4:22</a></i>;<br/>
<b>hence </b><a NAME="E3:26_1_1_2"/>
<font color="Maroon">IT</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="complex1.html#K17">|.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">seq</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c</font></span>)</span></span><a href="complex1.html#K17">.|</a></span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:26_1_1"/>
<font color="Maroon">IT</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="comseq_1.html#K9" target="_self">|.</a><span class="default"><font color="Maroon">seq</font></span><a href="comseq_1.html#K9" target="_self">.|</a></span>
 <b>by </b><i>, </i>;<br/>


</div>
