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<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="rewrite1.html#V2" title="REWRITE1:attr.2">weakly-normalizing</a> <a href="rewrite1.html#V4" title="REWRITE1:attr.4">with_UN_property</a> <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<a NAME="E1:80"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> or  not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> )
 
;<br/>
<a NAME="E2:80"/><b>then </b>
( <font color="Maroon" title="c2">a</font> <a href="rewrite1.html#R9" title="REWRITE1:pred.9">has_a_normal_form_wrt</a> <font color="Maroon" title="c1">R</font> &amp; ( for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">b</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b2">c</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font> holds <br/><font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">c</font> ) )
 
<b>by </b><i><a class="ref" href="rewrite1.html#D14" target="_self" title="REWRITE1:def.14">Def14</a>, <a class="ref" href="rewrite1.html#T47" target="_self" title="REWRITE1:th.47">Th47</a>, <a class="ref" href="rewrite1.html#T54" target="_self" title="REWRITE1:th.54">Th54</a></i>;<br/>
<b>hence </b><a NAME="E3:80"/>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#D12" target="_self" title="REWRITE1:def.12">Def12</a></i>;<br/>


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