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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th22</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: LOPBAN15:20</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><br/>  for <font color="Olive" title="b3">X1</font>, <font color="Olive" title="b4">Y1</font> being    <a href="rlsub_1.html#M1" title="RLSUB_1:mode.1">Subspace</a> of <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>,<font color="Olive" title="b2">Y</font></span><a href="prvect_3.html#K6" title="PRVECT_3:func.6">:]</a></span>  st <font color="Olive" title="b3">X1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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> &amp; <font color="Olive" title="b4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prvect_3.html#K6" title="PRVECT_3:func.6">[:</a><span class="default"><span class="p2">(<span class="default"><a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <font color="Olive" title="b1">X</font></span>)</span>,<font color="Olive" title="b2">Y</font></span><a href="prvect_3.html#K6" title="PRVECT_3:func.6">:]</a></span> holds <br/>( <font color="Olive" title="b3">X1</font> <a href="rlsub_2.html#K1" title="RLSUB_2:func.1">+</a> <font color="Olive" title="b4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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>,<font color="Olive" title="b2">Y</font></span><a href="prvect_3.html#K6" title="PRVECT_3:func.6">:]</a></span> &amp; <font color="Olive" title="b3">X1</font> <a href="rlsub_2.html#K2" title="RLSUB_2:func.2">/\</a> <font color="Olive" title="b4">Y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlsub_1.html#K1" title="RLSUB_1:func.1">(0).</a> <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>,<font color="Olive" title="b2">Y</font></span><a href="prvect_3.html#K6" title="PRVECT_3:func.6">:]</a></span> )</div></div>
