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<b>let </b><font color="Maroon">F1</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">F2</font> be    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">G</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:25_1_2"/><i><font color="Green">E39</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E2:25_1_2"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">k</font></span>)</span> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_4.html#K2" target="_self">@</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">k</font></span>)</span></span>)</span>
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E3:25_1_2"/><i><font color="Green">E41</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">F2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E4:25_1_2"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">k</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font> holds <br/><font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">k</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">k</font></span>)</span> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_4.html#K2" target="_self">@</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">k</font></span>)</span></span>)</span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:25_1_2_1"/>
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font></span>)</span>
 ;<br/><a NAME="E2:25_1_2_1"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> = 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span> <a href="group_1.html#K6">|^</a> <span class="p1">(<span class="default"><a href="group_4.html#K2" target="_self">@</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">k</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:25_1_2"/>
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font>
 <b>by </b><i>, , <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


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