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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <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"> ( <font color="Maroon" title="c1">R</font> is  <a href="rewrite1.html#V6" title="REWRITE1:attr.6">subcommutative</a>  implies <font color="Maroon" title="c1">R</font> is  <a href="rewrite1.html#V7" title="REWRITE1:attr.7">confluent</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:75_3_1"/>
<font color="Maroon" title="c1">R</font> is  <a href="rewrite1.html#V6" title="REWRITE1:attr.6">subcommutative</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">R</font> is  <a href="rewrite1.html#V7" title="REWRITE1:attr.7">confluent</a> </span><br/>

<a NAME="E2:75_3_1"/><span class="kw">then </span>
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">R</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">R</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a> <font color="Maroon" title="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T50" target="_self" title="REWRITE1:th.50">Th50</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:75_3_1"/>
<font color="Maroon" title="c1">R</font> is  <a href="rewrite1.html#V7" title="REWRITE1:attr.7">confluent</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rewrite1.html#T52" target="_self" title="REWRITE1:th.52">Th52</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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