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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th23</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: LOPBAN15:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>  ex <font color="Olive" title="b3">f</font> being   <a href="lopban_1.html#NM1" title="LOPBAN_1:NM.1">LinearOperator</a> of <font color="Olive" title="b1">X</font>,<span class="p1"><a href="prvect_3.html#K6" title="PRVECT_3:func.6">[:</a><span class="default"><font color="Olive" title="b1">X</font>,<span class="p2">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Olive" title="b2">Y</font></span>)</span></span><a href="prvect_3.html#K6" title="PRVECT_3:func.6">:]</a></span> st <br/>( <font color="Olive" title="b3">f</font> is  <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a>  &amp; (  for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">X</font> holds  <font color="Olive" title="b3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_3.html#K7" title="PRVECT_3:func.7">[</a><span class="default"><font color="Olive" title="b4">x</font>,<span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b2">Y</font></span>)</span></span><a href="prvect_3.html#K7" title="PRVECT_3:func.7">]</a></span> ) )</div></div>
