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<b>let </b><font color="Maroon">R</font> be  <a href="rewrite1.html#V2" target="_self">weakly-normalizing</a> <a href="rewrite1.html#V4" target="_self">with_UN_property</a> <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/>



<a NAME="E1:81"/><i><font color="Green">E21</font></i>: 
(  <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">a</font>,<font color="Maroon">R</font> <a href="rewrite1.html#R4" target="_self">is_a_normal_form_of</a> <font color="Maroon">a</font>,<font color="Maroon">R</font> &amp;  <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">b</font>,<font color="Maroon">R</font> <a href="rewrite1.html#R4" target="_self">is_a_normal_form_of</a> <font color="Maroon">b</font>,<font color="Maroon">R</font> )
 
<b>by </b><i><a class="ref" href="rewrite1.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E2:81"/><b>then </b><i><font color="Green">E29</font></i>: 
(  <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">a</font>,<font color="Maroon">R</font> <a href="rewrite1.html#R3" target="_self">is_a_normal_form_wrt</a> <font color="Maroon">R</font> &amp;  <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">b</font>,<font color="Maroon">R</font> <a href="rewrite1.html#R3" target="_self">is_a_normal_form_wrt</a> <font color="Maroon">R</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:81"/>
( <font color="Maroon">R</font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">a</font>, <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">a</font>,<font color="Maroon">R</font> &amp; <font color="Maroon">R</font> <a href="rewrite1.html#R1" target="_self">reduces</a> <font color="Maroon">b</font>, <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">b</font>,<font color="Maroon">R</font> )
 
<b>by </b><i><a class="ref" href="rewrite1.html#T13" target="_self">Th13</a>, </i>;<br/>
<a NAME="E4:81"/><b>then </b><i><font color="Green">E31</font></i>: 
(  <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">a</font>,<font color="Maroon">R</font>,<font color="Maroon">a</font> <a href="rewrite1.html#R2" target="_self">are_convertible_wrt</a> <font color="Maroon">R</font> &amp; <font color="Maroon">b</font>, <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">b</font>,<font color="Maroon">R</font> <a href="rewrite1.html#R2" target="_self">are_convertible_wrt</a> <font color="Maroon">R</font> )
 
<b>by </b><i><a class="txt" href="rewrite1.html#E2:81"><i><font color="Green">E29</font></i></a></i>;<br/>
<b>assume </b><a NAME="E5:81"/>
<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>
 ;<br/>

<a NAME="E6:81"/><b>then </b>
 <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">a</font>,<font color="Maroon">R</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><a class="ref" href="rewrite1.html#T15" target="_self">Th15</a>, </i>;<br/>
<a NAME="E7:81"/><b>then </b>
 <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">a</font>,<font color="Maroon">R</font>, <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">b</font>,<font color="Maroon">R</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#T15" target="_self">Th15</a>, </i>;<br/>
<b>hence </b><a NAME="E8:81"/>
 <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">a</font>,<font color="Maroon">R</font> <a href="hidden.html#R1">=</a>  <a href="rewrite1.html#K2" target="_self">nf</a> <font color="Maroon">b</font>,<font color="Maroon">R</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T14" target="_self">Th14</a>, <a class="ref" href="rewrite1.html#T8" target="_self">Th8</a></i>;<br/>


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