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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: INTEGRA7:15</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">f</font>, <font color="Olive" title="b3">g</font>, <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 <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st (  for <font color="Olive" title="b6">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b6">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Olive" title="b5">G</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) &amp; <font color="Olive" title="b4">F</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">X</font> &amp; <font color="Olive" title="b5">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <font color="Olive" title="b3">g</font>,<font color="Olive" title="b1">X</font> holds <br/><font color="Olive" title="b4">F</font> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">/</a> <font color="Olive" title="b5">G</font> <a href="integra7.html#R1" title="INTEGRA7:pred.1">is_integral_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b5">G</font></span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default"><font color="Olive" title="b4">F</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b3">g</font></span>)</span></span>)</span> <a href="rfunct_1.html#K3" title="RFUNCT_1:func.3">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">G</font> <a href="valued_1.html#K20" title="VALUED_1:func.20">(#)</a> <font color="Olive" title="b5">G</font></span>)</span>,<font color="Olive" title="b1">X</font></div></div>
