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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a> <a href="lattice3.html#V1" title="LATTICE3:attr.1">with_suprema</a> <a href="abcmiz_0.html#V1" title="ABCMIZ_0:attr.1">Noetherian</a> non <a href="abcmiz_0.html#V4" title="ABCMIZ_0:attr.4">void</a> <a href="abcmiz_0.html#V9" title="ABCMIZ_0:attr.9">adj-structured</a> <a href="abcmiz_0.html#V14" title="ABCMIZ_0:attr.14">commutative</a>  <a href="abcmiz_0.html#L3" title="ABCMIZ_0:struct.3">TAS-structure</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being  <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font> holds  <font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b1">t</font>, <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Olive" title="b1">t</font></span><br/><b>let </b><font color="Maroon" title="c2">t</font> be   <a href="abcmiz_0.html#NM1" title="ABCMIZ_0:NM.1">type</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">t</font>, <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c2">t</font></span><br/>



<b>set </b><font color="Maroon" title="c3">R</font> = <font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> ;<br/>
<a NAME="E1:128"/>
<font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  is  <a href="rewrite1.html#V3" title="REWRITE1:attr.3">strongly-normalizing</a> <a href="rewrite1.html#V4" title="REWRITE1:attr.4">with_UN_property</a> <a href="rewrite1.html#V8" title="REWRITE1:attr.8">with_Church-Rosser_property</a> <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>
 
<b>by </b><i><a class="ref" href="abcmiz_0.html#T70" target="_self" title="ABCMIZ_0:th.70">Th70</a>, <a class="ref" href="abcmiz_0.html#T78" target="_self" title="ABCMIZ_0:th.78">Th78</a></i>;<br/>
<a NAME="E2:128"/><b>then </b>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">t</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> </span>)</span> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a> 
 
<b>by </b><i><a class="ref" href="rewrite1.html#T55" title="REWRITE1:th.55">REWRITE1:55</a></i>;<br/>
<b>hence </b><a NAME="E3:128"/>
<font color="Maroon" title="c1">T</font> <a href="abcmiz_0.html#K11" title="ABCMIZ_0:func.11">@--&gt;</a>  <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c2">t</font>, <a href="abcmiz_0.html#K12" title="ABCMIZ_0:func.12">radix</a> <font color="Maroon" title="c2">t</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#D6" title="REWRITE1:def.6">REWRITE1:def 6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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