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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: LOPBAN_1:12</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">Y</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a><br/>  for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">h</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="lopban_1.html#K5" title="LOPBAN_1:func.5">RealVectSpace</a> (<font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">Y</font>)</span>)</span><br/>  for <font color="Olive" title="b5">a</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> ( <font color="Olive" title="b4">h</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <font color="Olive" title="b3">f</font> iff  for <font color="Olive" title="b6">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">X</font> holds  <font color="Olive" title="b4">h</font> <a href="lopban_1.html#K6" title="LOPBAN_1:func.6">.</a> <font color="Olive" title="b6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">f</font> <a href="lopban_1.html#K6" title="LOPBAN_1:func.6">.</a> <font color="Olive" title="b6">x</font></span>)</span> ) <span class="kw">by</span> <span class="lab"><a class="ref" href="lopban_1.html#T2" target="_self" onmouseover="rs('lopban_1/T2')" onmouseout="rh()">Th2</a></span>;<br/></div></div>
