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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="lattice3.html#V1">with_suprema</a> <a href="abcmiz_0.html#V1" target="_self">Noetherian</a> non <a href="abcmiz_0.html#V4" target="_self">void</a> <a href="abcmiz_0.html#V9" target="_self">adj-structured</a> <a href="abcmiz_0.html#V14" target="_self">commutative</a>  <a href="abcmiz_0.html#L3" target="_self">TAS-structure</a> ;<br/><b>let </b><font color="Maroon">t</font> be   <a href="abcmiz_0.html#NM1">type</a> of <font color="Maroon">T</font>;<br/>



<b>set </b><font color="Maroon">R</font> = <font color="Maroon">T</font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a> ;<br/>
<a NAME="E1:129"/>
<font color="Maroon">T</font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a>  is  <a href="rewrite1.html#V3">strongly-normalizing</a> <a href="rewrite1.html#V4">with_UN_property</a> <a href="rewrite1.html#V8">with_Church-Rosser_property</a> <a href="relat_1.html#NM1">Relation</a>
 
<b>by </b><i>, <a class="ref" href="abcmiz_0.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E2:129"/><b>then </b>
 <a href="rewrite1.html#K2">nf</a> <font color="Maroon">t</font>,<span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a> </span>)</span> <a href="rewrite1.html#R4">is_a_normal_form_of</a> <font color="Maroon">t</font>,<font color="Maroon">T</font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a> 
 
<b>by </b><i><a class="ref" href="rewrite1.html#T55">REWRITE1:55</a></i>;<br/>
<a NAME="E3:129"/><b>then </b>
<font color="Maroon">T</font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a>  <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">t</font>, <a href="rewrite1.html#K2">nf</a> <font color="Maroon">t</font>,<span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="rewrite1.html#D6">REWRITE1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E4:129"/>
<font color="Maroon">T</font> <a href="abcmiz_0.html#K11" target="_self">@--&gt;</a>  <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">t</font>, <a href="abcmiz_0.html#K12" target="_self">radix</a> <font color="Maroon">t</font>
 ;<br/>


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