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

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

<b>assume </b><a NAME="E1:76_4_1"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">R</font> is <a href="rewrite1.html#V8" target="_self">with_Church-Rosser_property</a>
 ;<br/>

<b>let </b><font color="Maroon">b</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D20" target="_self">REWRITE1:def 20</a><br/>

<b>assume </b><a NAME="E2:76_4_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">b</font> <a href="rewrite1.html#R3" target="_self">is_a_normal_form_wrt</a> <font color="Maroon">R</font>
 ;<br/>

<b>assume </b><a NAME="E3:76_4_1"/>
<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>
 ;<br/>

<a NAME="E4:76_4_1"/><b>then </b>
<font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="rewrite1.html#R5" target="_self">are_convergent_wrt</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="rewrite1.html#D3" target="_self">Def3</a>, </i>;<br/>
<b>then consider </b><font color="Maroon">c</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:76_4_1"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">R</font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">R</font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E7:76_4_1"/>
<font color="Maroon">R</font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#D4" target="_self">Def4</a>, <a class="ref" href="rewrite1.html#T12" target="_self">Th12</a>, </i>;<br/>


</div>
