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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th18</font></span>: <a NAME="T19"><span class="comment"><font color="firebrick">:: PUA2MSS1:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">partial</a>   <a href="unialg_1.html#V4" title="UNIALG_1:attr.4">non-empty</a>   <a href="unialg_1.html#L1" title="UNIALG_1:struct.1">UAStr</a> <br/>  for <font color="Olive" title="b2">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b2">R</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="pua2mss1.html#K6" title="PUA2MSS1:func.6">DomRel</a> <font color="Olive" title="b1">A</font> holds <br/>( <font color="Olive" title="b2">R</font> <a href="pua2mss1.html#K7" title="PUA2MSS1:func.7">|^</a> <font color="Olive" title="b1">A</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  &amp; <font color="Olive" title="b2">R</font> <a href="pua2mss1.html#K7" title="PUA2MSS1:func.7">|^</a> <font color="Olive" title="b1">A</font> is  <a href="relat_2.html#V3" title="RELAT_2:attr.3">symmetric</a>  &amp; <font color="Olive" title="b2">R</font> <a href="pua2mss1.html#K7" title="PUA2MSS1:func.7">|^</a> <font color="Olive" title="b1">A</font> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a>  )</div></div>
