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<b>let </b><font color="Maroon">z1</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">L</font>, <font color="Maroon">z2</font> be   <a href="struct_0.html#NM7">FinSequence</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><a NAME="E1:17_1_2"/><i><font color="Green">E34</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">z1</font> holds <br/> ex <font color="Olive">p</font> being  <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> &amp; <font color="Maroon">z1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> ) ) )
 ;<br/>

<b>assume </b><a NAME="E2:17_1_2"/><i><font color="Green">E36</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">z2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">F</font> &amp; ( for <font color="Olive">j</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">z2</font> holds <br/> ex <font color="Olive">p</font> being  <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> &amp; <font color="Maroon">z2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> <a href="hidden.html#R1">=</a> <font color="Olive">p</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> ) ) )
 ;<br/>

<i><font color="Green">E37</font></i>:  <a href="relset_1.html#K4">dom</a> <font color="Maroon">z1</font> = 
 <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>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
<br/>.= 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">z2</font>
<b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:17_1_2_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">k</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">z1</font>
 ;<br/><b>then consider </b><font color="Maroon">p1</font> being   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:17_1_2_2"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> &amp; <font color="Maroon">z1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> )
 <b>by </b><i/>;<br/><b>consider </b><font color="Maroon">p2</font> being   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E5:17_1_2_2"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> &amp; <font color="Maroon">z2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">i</font> )
 <b>by </b><i>, , </i>;<br/><b>thus </b><a NAME="E6:17_1_2_2"/>
<font color="Maroon">z1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">k</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:17_1_2"/>
<font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z2</font>
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


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