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<div><span class="kw">theorem </span><a NAME="T170"><span class="comment"><font color="firebrick">:: ABSRED_0:170</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">partial</a>   <a href="unialg_1.html#V3" title="UNIALG_1:attr.3">quasi_total</a>   <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">non-empty</a>   <a href="absred_0.html#V15" title="ABSRED_0:attr.15">Group-like</a>   <a href="absred_0.html#V16" title="ABSRED_0:attr.16">invariant</a>   <a href="absred_0.html#L2" title="ABSRED_0:struct.2">TRSStr</a> <br/>  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b1">S</font> is  <a href="absred_0.html#V18" title="ABSRED_0:attr.18">(R1)</a>  &amp; <font color="Olive" title="b1">S</font> is  <a href="absred_0.html#V20" title="ABSRED_0:attr.20">(R3)</a>  &amp; <font color="Olive" title="b1">S</font> is  <a href="absred_0.html#V23" title="ABSRED_0:attr.23">(R6)</a>  holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a</font> <a href="absred_0.html#K7" title="ABSRED_0:func.7">"</a></span>)</span> <a href="absred_0.html#K7" title="ABSRED_0:func.7">"</a></span>)</span> <a href="absred_0.html#K8" title="ABSRED_0:func.8">*</a> <font color="Olive" title="b3">b</font> <a href="absred_0.html#R10" title="ABSRED_0:pred.10">&lt;&lt;&gt;&gt;</a> <font color="Olive" title="b2">a</font> <a href="absred_0.html#K8" title="ABSRED_0:func.8">*</a> <font color="Olive" title="b3">b</font></div></div>
