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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th53</font></span>: <a NAME="T53"><span class="comment"><font color="firebrick">:: VFUNCT_1:53</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">Y</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">f</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>  st <font color="Olive" title="b4">f</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() holds <br/>( <span class="p1"><a href="normsp_0.html#K4" title="NORMSP_0:func.4">||.</a><span class="default"><font color="Olive" title="b4">f</font></span><a href="normsp_0.html#K4" title="NORMSP_0:func.4">.||</a></span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() &amp; <span class="p1">(<span class="default"><a href="vfunct_1.html#K5" title="VFUNCT_1:func.5">-</a> <font color="Olive" title="b4">f</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">Y</font> is <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() )</div></div>
