<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">f</font> be    <a href="prvect_1.html#M2" target="_self">UnOps</a> of  <a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font>, <font color="Maroon">h</font> be    <a href="prvect_1.html#M2" target="_self">UnOps</a> of  <a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:57_2_2"/><i><font color="Green">E60</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> holds  <font color="Maroon">f</font> <a href="prvect_1.html#K11" target="_self">.</a> <font color="Olive">i</font> <a href="funct_2.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Olive">i</font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:57_2_2"/><i><font color="Green">E61</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">h</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> holds  <font color="Maroon">h</font> <a href="prvect_1.html#K11" target="_self">.</a> <font color="Olive">i</font> <a href="funct_2.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Olive">i</font></span>)</span> ) )
 ;<br/>

<b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font>, <font color="Maroon">h'</font> = <font color="Maroon">h</font> as   <a href="finseq_1.html#NM1">FinSequence</a> ;<br/>
<a NAME="E4:57_2_2"/><i><font color="Green">E72</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</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> &amp;  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">h'</font> <a href="hidden.html#R1">=</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">h'</font></span>)</span> )
 
<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="57_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:57_2_2_1"/>
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">f'</font>
 ;<br/><b>then reconsider </b><font color="Maroon">i'</font> = <font color="Maroon">i</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" target="_self">carr</a> <font color="Maroon">g</font></span>)</span> <b>by </b><i>, <a class="ref" href="finseq_3.html#T31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:57_2_2_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="prvect_1.html#K17" target="_self">.</a> <font color="Maroon">i'</font></span>)</span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:57_2_2_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E9"><i><font color="Green">Lemma34</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:57_2_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font>
 <b>by </b><i>, <a class="txt" href="prvect_1.html#E9"><i><font color="Green">Lemma34</font></i></a>, <a class="ref" href="prvect_1.html#T11" target="_self">Th11</a>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>


</div>
