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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E4">Th6</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: MESFUNC2:6</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">r</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a><br/>  for <font color="Olive" title="b3">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="b4">f</font>, <font color="Olive" title="b5">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#K6" title="NUMBERS:func.6">ExtREAL</a><br/>  for <font color="Olive" title="b6">A</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b3">S</font>  st <font color="Olive" title="b4">f</font> is <font color="Olive" title="b6">A</font> <a href="mesfunc1.html#V1" title="MESFUNC1:attr.1">-measurable</a>  &amp; <font color="Olive" title="b5">g</font> is <font color="Olive" title="b6">A</font> <a href="mesfunc1.html#V1" title="MESFUNC1:attr.1">-measurable</a>  holds <br/> ex <font color="Olive" title="b7">F</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="numbers.html#K3" title="NUMBERS:func.3">RAT</a>,<font color="Olive" title="b3">S</font> st <br/> for <font color="Olive" title="b8">p</font> being   <a href="rat_1.html#NM1" title="RAT_1:NM.1">Rational</a> holds  <font color="Olive" title="b7">F</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b8">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="mesfunc1.html#K14" title="MESFUNC1:func.14">less_dom</a> (<font color="Olive" title="b4">f</font>,<font color="Olive" title="b8">p</font>)</span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="mesfunc1.html#K14" title="MESFUNC1:func.14">less_dom</a> (<font color="Olive" title="b5">g</font>,<span class="p3">(<span class="default"><font color="Olive" title="b2">r</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b8">p</font></span>)</span>)</span>)</span></span>)</span></div></div>
