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<div><span class="kw">theorem </span><a NAME="T11"><span class="comment"><font color="firebrick">:: MEASURE1:11</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   <a href="prob_1.html#NM1" title="PROB_1:NM.1">Field_Subset</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">M</font> being   <a href="measure1.html#NM1" title="MEASURE1:NM.1">Measure</a> of <font color="Olive" title="b2">S</font> holds <br/> (  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b1">X</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="b4">A</font>, <font color="Olive" title="b5">B</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b5">B</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="b1">X</font> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <font color="Olive" title="b4">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b4">A</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b5">B</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">S</font> &amp; <font color="Olive" title="b4">A</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Olive" title="b5">B</font> <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="measure1.html#D1" target="_self" onmouseover="rs('measure1/D1')" onmouseout="rh()">Def1</a>, <a class="ref" href="finsub_1.html#D1" onmouseover="rs('finsub_1/D1')" onmouseout="rh()">FINSUB_1:def 1</a>, <a class="ref" href="finsub_1.html#D2" onmouseover="rs('finsub_1/D2')" onmouseout="rh()">FINSUB_1:def 2</a>, <a class="ref" href="prob_1.html#T4" onmouseover="rs('prob_1/T4')" onmouseout="rh()">PROB_1:4</a>, <a class="ref" href="prob_1.html#T5" onmouseover="rs('prob_1/T5')" onmouseout="rh()">PROB_1:5</a></span>;<br/></div></div>
