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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E6">Th6</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: RANDOM_2:6</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">f</font>, <font color="Olive" title="b3">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> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> 2 <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> 2</span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p2">(<span class="default">2 <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p3">(<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="b3">g</font></span>)</span></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g</font> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> 2</span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> 2 <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">f</font> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> 2</span>)</span> <a href="valued_1.html#K47" title="VALUED_1:func.47">-</a> <span class="p2">(<span class="default">2 <a href="valued_1.html#K26" title="VALUED_1:func.26">(#)</a> <span class="p3">(<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="b3">g</font></span>)</span></span>)</span></span>)</span> <a href="valued_1.html#K3" title="VALUED_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">g</font> <a href="mesfun6c.html#K2" title="MESFUN6C:func.2">to_power</a> 2</span>)</span> )</div></div>
