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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="necklace.html#V1">symmetric</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:45"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 ;<br/>

<b>assume </b><a NAME="E2:45"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="rewrite1.html#M1">RedSequence</a> of the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:45"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="rewrite1.html#D3">REWRITE1:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="finseq_1.html#NM1">FinSequence</a> ;<br/>
<a NAME="E6:45"/><i><font color="Green">E26</font></i>: 
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a> 
 
<b>by </b><i><a class="ref" href="relat_2.html#T30">RELAT_2:30</a></i>;<br/>
<a NAME="E7:45"/><i><font color="Green">E27</font></i>: 
( <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <span class="p1">(<span class="default"><a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E4:45"><i><font color="Green">E25</font></i></a>, <a class="ref" href="finseq_5.html#T65">FINSEQ_5:65</a></i>;<br/>
<a NAME="E8:45"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> =  <a href="finseq_5.html#K3">Rev</a> <font color="Maroon">c<sub>7</sub></font> as    <a href="rewrite1.html#M1">RedSequence</a> of the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="neckla_3.html#E6:45"><i><font color="Green">E26</font></i></a>, <a class="ref" href="rewrite1.html#T10">REWRITE1:10</a></i>;<br/>
<a NAME="E2:45_1"/>
( <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="neckla_3.html#E7:45"><i><font color="Green">E27</font></i></a>, <a class="ref" href="finseq_5.html#D3">FINSEQ_5:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:45_1"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="rewrite1.html#D3">REWRITE1:def 3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:45"/>
the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</sub></font>
 ;<br/>


</div>
