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<span class="kw">let </span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds   <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Olive" title="b1">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="Olive" title="b1">a</font>,<font color="Maroon" title="c1">R</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <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></span><br/>



<a NAME="E1:78"/>
( <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="E2:78"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A1</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><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></span>;<br/>
<a NAME="E3:78"/>
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T54" target="_self" title="REWRITE1:th.54">Th54</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:78"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:78"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="rewrite1.html#D12" target="_self" title="REWRITE1:def.12">Def12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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