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<div><span class="kw">theorem </span><a NAME="T2"><span class="comment"><font color="firebrick">:: CIRCTRM1:2</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>   non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> <br/>  for <font color="Olive" title="b2">V</font> being  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V2</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">S</font> <a href="msaterm.html#K1" title="MSATERM:func.1">-Terms</a> <font color="Olive" title="b2">V</font></span>)</span> holds <br/> ( <font color="Olive" title="b3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  iff  for <font color="Olive" title="b4">t</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b3">X</font> holds <br/> ( <font color="Olive" title="b4">t</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">root</a>  &amp;  not <font color="Olive" title="b4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Olive" title="b1">S</font>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">S</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_9.html#T25" onmouseover="rs('trees_9/T25')" onmouseout="rh()">TREES_9:25</a></span>;<br/></div></div>
