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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: MESFUNC6:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</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> <br/>  for <font color="Olive" title="b2">S</font> being   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Olive" title="b1">X</font><br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">X</font>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b5">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b6">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b3">f</font> is <font color="Olive" title="b5">A</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <font color="Olive" title="b4">g</font> is <font color="Olive" title="b5">A</font> <a href="mesfunc6.html#V1" title="MESFUNC6:attr.1">-measurable</a>  &amp; <font color="Olive" title="b5">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b4">g</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b5">A</font> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p2">(<span class="default"><a href="mesfunc1.html#K10" title="MESFUNC1:func.10">less_dom</a> (<font color="Olive" title="b3">f</font>,<font color="Olive" title="b6">r</font>)</span>)</span></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <span class="p1">(<span class="default"><a href="mesfunc1.html#K12" title="MESFUNC1:func.12">great_dom</a> (<font color="Olive" title="b4">g</font>,<font color="Olive" title="b6">r</font>)</span>)</span> <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="mesfunc1.html#T36" onmouseover="rs('mesfunc1/T36')" onmouseout="rh()">MESFUNC1:36</a></span>;<br/></div></div>
