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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: PROB_1:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b2">S</font> is   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">X</font> iff ( <font color="Olive" title="b2">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="setfam_1.html#K9" title="SETFAM_1:func.9">bool</a> <font color="Olive" title="b1">X</font> &amp; (  for <font color="Olive" title="b3">A1</font> being   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Olive" title="b1">X</font>  st  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Olive" title="b3">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">S</font> holds <br/> <a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Olive" title="b3">A1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> ) &amp; (  for <font color="Olive" title="b3">A</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> holds <br/><font color="Olive" title="b3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> ) ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#D1" target="_self" onmouseover="rs('prob_1/D1')" onmouseout="rh()">Def1</a>, <a class="ref" href="prob_1.html#D6" target="_self" onmouseover="rs('prob_1/D6')" onmouseout="rh()">Def6</a></span>;<br/></div></div>
