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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: MESFUNC1:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C</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> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <font color="Olive" title="b1">C</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">ExtREAL</a> holds <br/> (  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default">1 <a href="mesfunc1.html#K8" title="MESFUNC1:func.8">/</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="subset_1.html#K6" title="SUBSET_1:func.6">\</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="relat_1.html#K8" title="RELAT_1:func.8">"</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> &amp; (  for <font color="Olive" title="b3">c</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">C</font>  st <font color="Olive" title="b3">c</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default">1 <a href="mesfunc1.html#K8" title="MESFUNC1:func.8">/</a> <font color="Olive" title="b2">f</font></span>)</span> holds <br/><span class="p1">(<span class="default">1 <a href="mesfunc1.html#K8" title="MESFUNC1:func.8">/</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="supinf_2.html#K18" title="SUPINF_2:func.18">1.</a> <a href="extreal1.html#K2" title="EXTREAL1:func.2">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">f</font> <a href="supinf_2.html#K12" title="SUPINF_2:func.12">.</a> <font color="Olive" title="b3">c</font></span>)</span> ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="mesfunc1.html#D8" target="_self" onmouseover="rs('mesfunc1/D8')" onmouseout="rh()">Def9</a></span>;<br/></div></div>
