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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th25</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: MATRLIN2:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">V1</font> being   <a href="matrlin.html#V1" title="MATRLIN:attr.1">finite-dimensional</a>  <a href="vectsp_1.html#NM9" title="VECTSP_1:NM.9">VectSp</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">b1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b2">V1</font><br/>  for <font color="Olive" title="b4">W1</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Olive" title="b2">V1</font>  st <font color="Olive" title="b4">W1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Olive" title="b2">V1</font> holds <br/> for <font color="Olive" title="b5">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b4">W1</font><br/>  for <font color="Olive" title="b6">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Olive" title="b2">V1</font><br/>  for <font color="Olive" title="b7">w1</font> being    <a href="matrlin.html#M1" title="MATRLIN:mode.1">OrdBasis</a> of <font color="Olive" title="b4">W1</font>  st <font color="Olive" title="b6">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">w</font> &amp; <font color="Olive" title="b3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">w1</font> holds <br/><font color="Olive" title="b6">v</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Olive" title="b3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">w</font> <a href="matrlin.html#K9" title="MATRLIN:func.9">|--</a> <font color="Olive" title="b7">w1</font></div></div>
