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<div><span class="kw">theorem </span><a NAME="T30"><span class="comment"><font color="firebrick">:: VFUNCT_1:30</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">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="b3">V</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b4">f1</font>, <font color="Olive" title="b5">f2</font> being   <a href="struct_0.html#NM11" title="STRUCT_0:NM.11">PartFunc</a> of <font color="Olive" title="b2">C</font>,<font color="Olive" title="b3">V</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <font color="Olive" title="b5">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <font color="Olive" title="b5">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font></span>)</span> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <font color="Olive" title="b5">f2</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b4">f1</font> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <font color="Olive" title="b5">f2</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Olive" title="b4">f1</font> <a href="vfunct_1.html#K2" title="VFUNCT_1:func.2">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">f2</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">X</font></span>)</span> )</div></div>
