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

<b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">h</font> be    <a href="prvect_1.html#M2" title="PRVECT_1:mode.2">UnOps</a> of  <a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:54_2_2"/><i><font color="Green" title="E33">A6</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> holds  <font color="Maroon" title="c2">f</font> <a href="prvect_1.html#K11" title="PRVECT_1:func.11">.</a> <font color="Olive" title="b1">i</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K17" title="PRVECT_1:func.17">.</a> <font color="Olive" title="b1">i</font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:54_2_2"/><i><font color="Green" title="E34">A7</font></i>: 
(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> holds  <font color="Maroon" title="c3">h</font> <a href="prvect_1.html#K11" title="PRVECT_1:func.11">.</a> <font color="Olive" title="b1">i</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K17" title="PRVECT_1:func.17">.</a> <font color="Olive" title="b1">i</font></span>)</span> ) )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c4">f'</font> = <font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c5">h'</font> = <font color="Maroon" title="c3">h</font> as   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> ;<br/>
<a NAME="E4:54_2_2"/><i><font color="Green" title="E35">A8</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">f'</font></span>)</span> &amp;  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c5">h'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">h'</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">i</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>assume </b><a NAME="E1:54_2_2_1"/>
<font color="Maroon" title="c6">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c4">f'</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c7">i'</font> = <font color="Maroon" title="c6">i</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="prvect_1.html#K16" title="PRVECT_1:func.16">carr</a> <font color="Maroon" title="c1">g</font></span>)</span> <b>by </b><i><a class="txt" href="prvect_1.html#E1:54_2_2"><i><font color="Green" title="E33">A6</font></i></a>, <a class="ref" href="finseq_3.html#T31" title="FINSEQ_3:th.31">FINSEQ_3:31</a></i>;<br/><a NAME="E3:54_2_2_1"/>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">g</font> <a href="prvect_1.html#K17" title="PRVECT_1:func.17">.</a> <font color="Maroon" title="c7">i'</font></span>)</span>
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:54_2_2"><i><font color="Green" title="E33">A6</font></i></a></i>;<br/><b>hence </b><a NAME="E4:54_2_2_1"/>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">i</font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E2:54_2_2"><i><font color="Green" title="E34">A7</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:54_2_2"/>
<font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="txt" href="prvect_1.html#E1:54_2_2"><i><font color="Green" title="E33">A6</font></i></a>, <a class="txt" href="prvect_1.html#E2:54_2_2"><i><font color="Green" title="E34">A7</font></i></a>, <a class="txt" href="prvect_1.html#E4:54_2_2"><i><font color="Green" title="E35">A8</font></i></a>, <a class="ref" href="finseq_1.html#T17" title="FINSEQ_1:th.17">FINSEQ_1:17</a></i>;<br/>


</div>
