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<div class="add">

<b>let </b><font color="Maroon">A1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> , <font color="Maroon">A2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:83_1_2"/><i><font color="Green">E27</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">X</font> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">X</font> holds <br/><font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="roughs_1.html#K6" target="_self">MemberFunc</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="roughs_1.html#K1" target="_self">.</a> <font color="Olive">n</font></span>)</span>,<font color="Maroon">A</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> ) )
 <b>and </b><br/><a NAME="E2:83_1_2"/><i><font color="Green">E33</font></i>: 
(  <a href="relset_1.html#K4">dom</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">X</font> &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">X</font> holds <br/><font color="Maroon">A2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="roughs_1.html#K6" target="_self">MemberFunc</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="roughs_1.html#K1" target="_self">.</a> <font color="Olive">n</font></span>)</span>,<font color="Maroon">A</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> ) )
 ;<br/>

<a NAME="E3:83_1_2"/>
for <font color="Olive">n</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">A1</font> holds <br/><font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:83_1_2_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">A1</font>
 ;<br/>

<b>then </b><font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> = 
<span class="p1">(<span class="default"><a href="roughs_1.html#K6" target="_self">MemberFunc</a> <span class="p2">(<span class="default"><font color="Maroon">X</font> <a href="roughs_1.html#K1" target="_self">.</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">A</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="roughs_1.html#T5" target="_self">Th5</a></i>
<br/>.= 
<font color="Maroon">A2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
<b>by </b><i><a class="ref" href="roughs_1.html#T5" target="_self">Th5</a>, , </i>
;<br/>
<b>hence </b><a NAME="E3:83_1_2_1"/>
<font color="Maroon">A1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:83_1_2"/>
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font>
 <b>by </b><i><a class="ref" href="roughs_1.html#T5" target="_self">Th5</a>, , <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


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