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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> ;<br/>



<a NAME="E1:80"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> or  not <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font> )
 
;<br/>
<a NAME="E2:80"/><b>then </b>
( <font color="Maroon">a</font> <a href="rewrite1.html#R9" target="_self">has_a_normal_form_wrt</a> <font color="Maroon">R</font> &amp; ( for <font color="Olive">b</font>, <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">b</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; <font color="Olive">c</font> <a href="rewrite1.html#R4" target="_self">is_a_normal_form_of</a> <font color="Maroon">a</font>,<font color="Maroon">R</font> holds <br/><font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> ) )
 
<b>by </b><i>, , <a class="ref" href="rewrite1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E3:80"/>
 <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>
 <b>by </b><i/>;<br/>


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