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<b>let </b><font color="Maroon">R</font> be   <a href="relat_1.html#NM1">Relation</a>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<b>given </b><font color="Maroon">p</font> being    <a href="rewrite1.html#M1" target="_self">RedSequence</a> of <font color="Maroon">R</font><b> such that </b><a NAME="E1:35"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">p</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">p</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D3" target="_self">REWRITE1:def 3</a><br/>

<a NAME="E2:35"/>
<font color="Maroon">p</font> is    <a href="rewrite1.html#M1" target="_self">RedSequence</a> of <font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K4">~</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:35_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D2" target="_self">REWRITE1:def 2</a><br/>

<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="E2:35_1"/>
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp; <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> )
 ;<br/>

<a NAME="E3:35_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:35_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p3">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K4">~</a> </span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:35"/><b>then </b>
<font color="Maroon">R</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="relat_1.html#K4">~</a> </span>)</span> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:35"/>
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="rewrite1.html#R2" target="_self">are_convertible_wrt</a> <font color="Maroon">R</font>
 <b>by </b><i/>;<br/>

<b>hence </b><a NAME="E5:35"/>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="rewrite1.html#R2" target="_self">are_convertible_wrt</a> <font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T2" target="_self">Th2</a></i>;<br/>


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