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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">T</font> be  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#V2">admissible</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V9">Field-like</a> non <a href="vectsp_1.html#V10">degenerated</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">P</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span>;<br/>







<b>assume </b><a NAME="E1:20"/>
 <a href="polyred.html#K3">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font> is <a href="rewrite1.html#V4">with_UN_property</a>
 ;<br/>

<b>then reconsider </b><font color="Maroon">R</font> =  <a href="polyred.html#K3">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font> as  <a href="rewrite1.html#V2">weakly-normalizing</a> <a href="rewrite1.html#V4">with_UN_property</a> <a href="relat_1.html#NM1">Relation</a> ;<br/>
<a NAME="E3:20"/>
<font color="Maroon">R</font> is <a href="rewrite1.html#V8">with_Church-Rosser_property</a>
 
;<br/>
<b>hence </b><a NAME="E4:20"/>
 <a href="polyred.html#K3">PolyRedRel</a> <font color="Maroon">P</font>,<font color="Maroon">T</font> is <a href="rewrite1.html#V8">with_Church-Rosser_property</a>
 ;<br/>


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